Geraden und Ebenen

Eigenvektoren

Linearkombination

Lineare Unabhängigkeit

Erzeugendensystem, Basis

Orthogonale Projektion

Vektoren in neuer Basis darstellen

Winkel, Länge, Fläche, Volumen von Vektoren

Vektor aus Bedingungen ableiten

Anwendungen

Integralgleichung

kettenregel

Lösbarkeit einer Matrix

Glechgewicht

Schiefe Ebene

Elektrische Anlage mit Abzweigunen

Flächenträgheit

Wechselstrom

Cauchy Verdichtungssatz 

Schaltvorgänge

Singulärwertzerlegung

Spann

Lineares Gleichungssystem

spannung

LR-Zerlegung mit pivotisierung 

Basis bestimmen

trigonalisierbarkeit

Fourier Koeffizienten bestimmen

Reimann-Summen

Ungleichungen 

Statik in der Ebene

Fourier-Reihen

Funktionsfolgen

Unterschied In/Homogen

Basis, Basiswechsel

Abbildungsmatrizen

Funktionen bestimmen

Gruppen

lineare abbildung 

quadratische ergänzung

Baustatik 1

Anfangswertprobleme :)

Differentialgleichungen

basis 

QR-Algorithmus

QR-Zerlegung

Cholesky-Zerlegung

Bild & Urbild

Zweigstromanalyse

Transistor als Thermometer

Investment

Teilfolgen

Epsilon Delta Kriterium

prinzip der virtuellen verrückung 

Linear Kombination

Folgen, Reihen und Potenzreihen

Flächenpressung

Arbeit 

Cholesky Zerlegung

Polynomfunktionen beschreiben

Zu Maß-und Integrationstheorie: Majorisierte Konvergenz

Teilchenphysik und Festkörperphysik

Orthogonaltrajektorien

test

Taylorreihen

Regel von de L'Hopital

Mathe

KRAFT

Grenzwert Funktion 

Folgenkriterium

ϵ-δ Kriterium 

Beweis Stetigkeit 

Wahrheitstabelle

2x2 Matrix

Matrix invertieren

Basiswechselsatz

Lineare Abbildunge 

Vorderrad fahradgabel lagerkräfte berechnen 

Spannungsregelung

Jordan Normal Form

Test

Induktion 

Jordan-Normalform

Ansatz der Störfunktion zur Bestimmung der Partikulären Lösung

Kurvenintegral

dlg mithilfe inhomogenen linearen system lösen

Inverse einer Matrix

Gleichmäßige Stetigkeit

addition

Regel von L´Hospital

Lineare Abbildungen

dimension eines Untervektorraumes bestimmen

Stationäre Stoffübertragung

Polplan, Prinzip der virtuellen Verrückungen

komplexe Ungleichungen 

Bidualräume

Dualräume

Taylorpolynome

Kern und Basis

Diagonalisieren einer Matrix

Rekursive Folgen

Exponentialreihe

Darstellungsmatrizen

restglied

Basiswechsel

Gamma Funktion

<p>\[\begin{align*}\left(\begin{array}{l}</p>
<p>1 \\</p>
<p>1 \\</p>
<p>0</p>
<p>\end{array}\right) \times\left(\begin{array}{l}</p>
<p>1 \\</p>
<p>1 \\</p>
<p>1</p>
<p>\end{array}\right)&amp;=\left(\begin{array}{r}</p>
<p>1 \\</p>
<p>-1 \\</p>
<p>0</p>
<p>\end{array}\right)\end{align*}\]</p>
<p>Die Länge beträgt $\sqrt{2}$ und ist als Fläche zwischen den Vektoren $\left(\begin{array}{l}1 \\ 1 \\ 0\end{array}\right)$ und $\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right)$ zu interpretieren.</p>

<p><mjx-container class="MathJax" jax="SVG" display="true" justify="left"><svg alt="\begin{align*}\left(\begin{array}{l}
1 \\
1 \\
0
\end{array}\right) \times\left(\begin{array}{l}
1 \\
1 \\
1
\end{array}\right)&=\left(\begin{array}{r}
1 \\
-1 \\
0
\end{array}\right)\end{align*}" style="vertical-align: -3.733ex;" xmlns="http://www.w3.org/2000/svg" width="22.814ex" height="8.597ex" role="img" focusable="false" viewBox="0 -2150 10084 3800" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-29-TEX-S4-239B" d="M837 1154Q843 1148 843 1145Q843 1141 818 1106T753 1002T667 841T574 604T494 299Q417 -84 417 -609Q417 -641 416 -647T411 -654Q409 -655 366 -655Q299 -655 297 -654Q292 -652 292 -643T291 -583Q293 -400 304 -242T347 110T432 470T574 813T785 1136Q787 1139 790 1142T794 1147T796 1150T799 1152T802 1153T807 1154T813 1154H819H837Z"></path><path id="MJX-29-TEX-S4-239D" d="M843 -635Q843 -638 837 -644H820Q801 -644 800 -643Q792 -635 785 -626Q684 -503 605 -363T473 -75T385 216T330 518T302 809T291 1093Q291 1144 291 1153T296 1164Q298 1165 366 1165Q409 1165 411 1164Q415 1163 416 1157T417 1119Q417 529 517 109T833 -617Q843 -631 843 -635Z"></path><path id="MJX-29-TEX-S4-239C" d="M413 -9Q412 -9 407 -9T388 -10T354 -10Q300 -10 297 -9Q294 -8 293 -5Q291 5 291 127V300Q291 602 292 605L296 609Q298 610 366 610Q382 610 392 610T407 610T412 609Q416 609 416 592T417 473V127Q417 -9 413 -9Z"></path><path id="MJX-29-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-29-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-29-TEX-S4-239E" d="M31 1143Q31 1154 49 1154H59Q72 1154 75 1152T89 1136Q190 1013 269 873T401 585T489 294T544 -8T572 -299T583 -583Q583 -634 583 -643T577 -654Q575 -655 508 -655Q465 -655 463 -654Q459 -653 458 -647T457 -609Q457 -58 371 340T100 1037Q87 1059 61 1098T31 1143Z"></path><path id="MJX-29-TEX-S4-23A0" d="M56 -644H50Q31 -644 31 -635Q31 -632 37 -622Q69 -579 100 -527Q286 -228 371 170T457 1119Q457 1161 462 1164Q464 1165 520 1165Q575 1165 577 1164Q582 1162 582 1153T583 1093Q581 910 570 752T527 400T442 40T300 -303T89 -626Q78 -640 75 -642T61 -644H56Z"></path><path id="MJX-29-TEX-S4-239F" d="M579 -9Q578 -9 573 -9T554 -10T520 -10Q466 -10 463 -9Q460 -8 459 -5Q457 5 457 127V300Q457 602 458 605L462 609Q464 610 532 610Q548 610 558 610T573 610T578 609Q582 609 582 592T583 473V127Q583 -9 579 -9Z"></path><path id="MJX-29-TEX-N-D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path><path id="MJX-29-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-29-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr"><g data-mml-node="mtd"><g data-mml-node="mrow"><g data-mml-node="mo"><use data-c="239B" xlink:href="#MJX-29-TEX-S4-239B" transform="translate(0,996)"></use><use data-c="239D" xlink:href="#MJX-29-TEX-S4-239D" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239C" xlink:href="#MJX-29-TEX-S4-239C" transform="scale(1,0.924)"></use></svg></g><g data-mml-node="mtable" transform="translate(875,0)"><g data-mml-node="mtr" 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transform="translate(3472.4,0)"><g data-mml-node="mo"><use data-c="239B" xlink:href="#MJX-29-TEX-S4-239B" transform="translate(0,996)"></use><use data-c="239D" xlink:href="#MJX-29-TEX-S4-239D" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239C" xlink:href="#MJX-29-TEX-S4-239C" transform="scale(1,0.924)"></use></svg></g><g data-mml-node="mtable" transform="translate(875,0)"><g data-mml-node="mtr" transform="translate(0,1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-29-TEX-N-31"></use></g></g></g><g data-mml-node="mtr"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-29-TEX-N-31"></use></g></g></g><g data-mml-node="mtr" transform="translate(0,-1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-29-TEX-N-31"></use></g></g></g></g><g data-mml-node="mo" transform="translate(1375,0)"><use data-c="239E" xlink:href="#MJX-29-TEX-S4-239E" transform="translate(0,996)"></use><use data-c="23A0" xlink:href="#MJX-29-TEX-S4-23A0" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239F" xlink:href="#MJX-29-TEX-S4-239F" transform="scale(1,0.924)"></use></svg></g></g></g><g data-mml-node="mtd" transform="translate(5722.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><use data-c="3D" xlink:href="#MJX-29-TEX-N-3D"></use></g><g data-mml-node="mrow" transform="translate(1333.6,0)"><g data-mml-node="mo"><use data-c="239B" xlink:href="#MJX-29-TEX-S4-239B" transform="translate(0,996)"></use><use data-c="239D" xlink:href="#MJX-29-TEX-S4-239D" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239C" xlink:href="#MJX-29-TEX-S4-239C" transform="scale(1,0.924)"></use></svg></g><g data-mml-node="mtable" transform="translate(875,0)"><g 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<p>Die Länge beträgt <mjx-container class="MathJax" jax="SVG"><svg alt="\sqrt{2}" style="vertical-align: -0.225ex;" xmlns="http://www.w3.org/2000/svg" width="3.061ex" height="2.398ex" role="img" focusable="false" viewBox="0 -960.5 1353 1060" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-30-TEX-N-221A" d="M95 178Q89 178 81 186T72 200T103 230T169 280T207 309Q209 311 212 311H213Q219 311 227 294T281 177Q300 134 312 108L397 -77Q398 -77 501 136T707 565T814 786Q820 800 834 800Q841 800 846 794T853 782V776L620 293L385 -193Q381 -200 366 -200Q357 -200 354 -197Q352 -195 256 15L160 225L144 214Q129 202 113 190T95 178Z"></path><path id="MJX-30-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msqrt"><g transform="translate(853,0)"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-30-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(0,100.5)"><use data-c="221A" xlink:href="#MJX-30-TEX-N-221A"></use></g><rect width="500" height="60" x="853" y="840.5"></rect></g></g></g></svg></mjx-container> und ist als Fläche zwischen den Vektoren <mjx-container class="MathJax" jax="SVG"><svg alt="\left(\begin{array}{l}1 \\ 1 \\ 0\end{array}\right)" style="vertical-align: -3.733ex;" xmlns="http://www.w3.org/2000/svg" width="5.09ex" height="8.597ex" role="img" focusable="false" viewBox="0 -2150 2250 3800" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-31-TEX-S4-239B" d="M837 1154Q843 1148 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data-c="31" xlink:href="#MJX-31-TEX-N-31"></use></g></g></g><g data-mml-node="mtr"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-31-TEX-N-31"></use></g></g></g><g data-mml-node="mtr" transform="translate(0,-1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="30" xlink:href="#MJX-31-TEX-N-30"></use></g></g></g></g><g data-mml-node="mo" transform="translate(1375,0)"><use data-c="239E" xlink:href="#MJX-31-TEX-S4-239E" transform="translate(0,996)"></use><use data-c="23A0" xlink:href="#MJX-31-TEX-S4-23A0" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239F" xlink:href="#MJX-31-TEX-S4-239F" transform="scale(1,0.924)"></use></svg></g></g></g></g></svg></mjx-container> und <mjx-container class="MathJax" jax="SVG"><svg alt="\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right)" style="vertical-align: -3.733ex;" xmlns="http://www.w3.org/2000/svg" width="5.09ex" height="8.597ex" role="img" focusable="false" viewBox="0 -2150 2250 3800" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-32-TEX-S4-239B" d="M837 1154Q843 1148 843 1145Q843 1141 818 1106T753 1002T667 841T574 604T494 299Q417 -84 417 -609Q417 -641 416 -647T411 -654Q409 -655 366 -655Q299 -655 297 -654Q292 -652 292 -643T291 -583Q293 -400 304 -242T347 110T432 470T574 813T785 1136Q787 1139 790 1142T794 1147T796 1150T799 1152T802 1153T807 1154T813 1154H819H837Z"></path><path id="MJX-32-TEX-S4-239D" d="M843 -635Q843 -638 837 -644H820Q801 -644 800 -643Q792 -635 785 -626Q684 -503 605 -363T473 -75T385 216T330 518T302 809T291 1093Q291 1144 291 1153T296 1164Q298 1165 366 1165Q409 1165 411 1164Q415 1163 416 1157T417 1119Q417 529 517 109T833 -617Q843 -631 843 -635Z"></path><path id="MJX-32-TEX-S4-239C" d="M413 -9Q412 -9 407 -9T388 -10T354 -10Q300 -10 297 -9Q294 -8 293 -5Q291 5 291 127V300Q291 602 292 605L296 609Q298 610 366 610Q382 610 392 610T407 610T412 609Q416 609 416 592T417 473V127Q417 -9 413 -9Z"></path><path id="MJX-32-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-32-TEX-S4-239E" d="M31 1143Q31 1154 49 1154H59Q72 1154 75 1152T89 1136Q190 1013 269 873T401 585T489 294T544 -8T572 -299T583 -583Q583 -634 583 -643T577 -654Q575 -655 508 -655Q465 -655 463 -654Q459 -653 458 -647T457 -609Q457 -58 371 340T100 1037Q87 1059 61 1098T31 1143Z"></path><path id="MJX-32-TEX-S4-23A0" d="M56 -644H50Q31 -644 31 -635Q31 -632 37 -622Q69 -579 100 -527Q286 -228 371 170T457 1119Q457 1161 462 1164Q464 1165 520 1165Q575 1165 577 1164Q582 1162 582 1153T583 1093Q581 910 570 752T527 400T442 40T300 -303T89 -626Q78 -640 75 -642T61 -644H56Z"></path><path id="MJX-32-TEX-S4-239F" d="M579 -9Q578 -9 573 -9T554 -10T520 -10Q466 -10 463 -9Q460 -8 459 -5Q457 5 457 127V300Q457 602 458 605L462 609Q464 610 532 610Q548 610 558 610T573 610T578 609Q582 609 582 592T583 473V127Q583 -9 579 -9Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mrow"><g data-mml-node="mo"><use data-c="239B" xlink:href="#MJX-32-TEX-S4-239B" transform="translate(0,996)"></use><use data-c="239D" xlink:href="#MJX-32-TEX-S4-239D" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239C" xlink:href="#MJX-32-TEX-S4-239C" transform="scale(1,0.924)"></use></svg></g><g data-mml-node="mtable" transform="translate(875,0)"><g data-mml-node="mtr" transform="translate(0,1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-32-TEX-N-31"></use></g></g></g><g data-mml-node="mtr"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-32-TEX-N-31"></use></g></g></g><g data-mml-node="mtr" transform="translate(0,-1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-32-TEX-N-31"></use></g></g></g></g><g data-mml-node="mo" transform="translate(1375,0)"><use data-c="239E" xlink:href="#MJX-32-TEX-S4-239E" transform="translate(0,996)"></use><use data-c="23A0" xlink:href="#MJX-32-TEX-S4-23A0" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239F" xlink:href="#MJX-32-TEX-S4-239F" transform="scale(1,0.924)"></use></svg></g></g></g></g></svg></mjx-container> zu interpretieren.</p>

<p>Bilde das Kreuzprodukt $\left(\begin{array}{l}1 \\ 1 \\ 0\end{array}\right) \times\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right)$:</p>


<p>Bilde das Kreuzprodukt <mjx-container class="MathJax" jax="SVG"><svg alt="\left(\begin{array}{l}1 \\ 1 \\ 0\end{array}\right) \times\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right)" style="vertical-align: -3.733ex;" xmlns="http://www.w3.org/2000/svg" width="12.947ex" height="8.597ex" role="img" focusable="false" viewBox="0 -2150 5722.4 3800" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-24-TEX-S4-239B" d="M837 1154Q843 1148 843 1145Q843 1141 818 1106T753 1002T667 841T574 604T494 299Q417 -84 417 -609Q417 -641 416 -647T411 -654Q409 -655 366 -655Q299 -655 297 -654Q292 -652 292 -643T291 -583Q293 -400 304 -242T347 110T432 470T574 813T785 1136Q787 1139 790 1142T794 1147T796 1150T799 1152T802 1153T807 1154T813 1154H819H837Z"></path><path id="MJX-24-TEX-S4-239D" d="M843 -635Q843 -638 837 -644H820Q801 -644 800 -643Q792 -635 785 -626Q684 -503 605 -363T473 -75T385 216T330 518T302 809T291 1093Q291 1144 291 1153T296 1164Q298 1165 366 1165Q409 1165 411 1164Q415 1163 416 1157T417 1119Q417 529 517 109T833 -617Q843 -631 843 -635Z"></path><path id="MJX-24-TEX-S4-239C" d="M413 -9Q412 -9 407 -9T388 -10T354 -10Q300 -10 297 -9Q294 -8 293 -5Q291 5 291 127V300Q291 602 292 605L296 609Q298 610 366 610Q382 610 392 610T407 610T412 609Q416 609 416 592T417 473V127Q417 -9 413 -9Z"></path><path id="MJX-24-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-24-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-24-TEX-S4-239E" d="M31 1143Q31 1154 49 1154H59Q72 1154 75 1152T89 1136Q190 1013 269 873T401 585T489 294T544 -8T572 -299T583 -583Q583 -634 583 -643T577 -654Q575 -655 508 -655Q465 -655 463 -654Q459 -653 458 -647T457 -609Q457 -58 371 340T100 1037Q87 1059 61 1098T31 1143Z"></path><path id="MJX-24-TEX-S4-23A0" d="M56 -644H50Q31 -644 31 -635Q31 -632 37 -622Q69 -579 100 -527Q286 -228 371 170T457 1119Q457 1161 462 1164Q464 1165 520 1165Q575 1165 577 1164Q582 1162 582 1153T583 1093Q581 910 570 752T527 400T442 40T300 -303T89 -626Q78 -640 75 -642T61 -644H56Z"></path><path id="MJX-24-TEX-S4-239F" d="M579 -9Q578 -9 573 -9T554 -10T520 -10Q466 -10 463 -9Q460 -8 459 -5Q457 5 457 127V300Q457 602 458 605L462 609Q464 610 532 610Q548 610 558 610T573 610T578 609Q582 609 582 592T583 473V127Q583 -9 579 -9Z"></path><path id="MJX-24-TEX-N-D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mrow"><g data-mml-node="mo"><use data-c="239B" xlink:href="#MJX-24-TEX-S4-239B" transform="translate(0,996)"></use><use data-c="239D" xlink:href="#MJX-24-TEX-S4-239D" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239C" xlink:href="#MJX-24-TEX-S4-239C" transform="scale(1,0.924)"></use></svg></g><g data-mml-node="mtable" transform="translate(875,0)"><g data-mml-node="mtr" transform="translate(0,1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-24-TEX-N-31"></use></g></g></g><g data-mml-node="mtr"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-24-TEX-N-31"></use></g></g></g><g data-mml-node="mtr" transform="translate(0,-1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="30" xlink:href="#MJX-24-TEX-N-30"></use></g></g></g></g><g data-mml-node="mo" transform="translate(1375,0)"><use data-c="239E" xlink:href="#MJX-24-TEX-S4-239E" transform="translate(0,996)"></use><use data-c="23A0" xlink:href="#MJX-24-TEX-S4-23A0" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239F" xlink:href="#MJX-24-TEX-S4-239F" transform="scale(1,0.924)"></use></svg></g></g><g data-mml-node="mo" transform="translate(2472.2,0)"><use data-c="D7" xlink:href="#MJX-24-TEX-N-D7"></use></g><g data-mml-node="mrow" transform="translate(3472.4,0)"><g data-mml-node="mo"><use data-c="239B" xlink:href="#MJX-24-TEX-S4-239B" transform="translate(0,996)"></use><use data-c="239D" xlink:href="#MJX-24-TEX-S4-239D" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239C" xlink:href="#MJX-24-TEX-S4-239C" transform="scale(1,0.924)"></use></svg></g><g data-mml-node="mtable" transform="translate(875,0)"><g data-mml-node="mtr" transform="translate(0,1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-24-TEX-N-31"></use></g></g></g><g data-mml-node="mtr"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-24-TEX-N-31"></use></g></g></g><g data-mml-node="mtr" transform="translate(0,-1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-24-TEX-N-31"></use></g></g></g></g><g data-mml-node="mo" transform="translate(1375,0)"><use data-c="239E" xlink:href="#MJX-24-TEX-S4-239E" transform="translate(0,996)"></use><use data-c="23A0" xlink:href="#MJX-24-TEX-S4-23A0" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239F" xlink:href="#MJX-24-TEX-S4-239F" transform="scale(1,0.924)"></use></svg></g></g></g></g></svg></mjx-container>:</p>


<p>\[\begin{align*}\left(\begin{array}{l}</p>
<p>1 \\</p>
<p>1 \\</p>
<p>0</p>
<p>\end{array}\right) \times\left(\begin{array}{l}</p>
<p>1 \\</p>
<p>1 \\</p>
<p>1</p>
<p>\end{array}\right)&amp;=\left(\begin{array}{l}</p>
<p>1 \cdot 1-0 \cdot 1 \\</p>
<p>0 \cdot 1-1 \cdot 1 \\</p>
<p>1 \cdot 1-1 \cdot 1</p>
<p>\end{array}\right) \\ \\</p>
<p>&amp;=\left(\begin{array}{r}</p>
<p>1 \\</p>
<p>-1 \\</p>
<p>0</p>
<p>\end{array}\right)\end{align*}\]</p>


<p>Berechne den Betrag (Länge) des neu entstandenen Vektors:</p>


<p>\[\begin{align*}\left| \left( \begin{array}{r}</p>
<p>1 \\</p>
<p>-1 \\</p>
<p>0</p>
<p>\end{array}\right) \right|=\sqrt{1+1+0}=\sqrt{2}\end{align*}\]</p>


<p>Wie ist die länge zu interpretieren?</p>


<p>Die Länge des Vektors entspricht der Fläche des durch die Vektoren $\left(\begin{array}{l}1 \\ 1 \\ 0\end{array}\right)$ und $\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right)$ aufgespannten Parallelogramms.</p>

<p>Die Länge des Vektors entspricht der Fläche des durch die Vektoren <mjx-container class="MathJax" jax="SVG"><svg alt="\left(\begin{array}{l}1 \\ 1 \\ 0\end{array}\right)" style="vertical-align: -3.733ex;" xmlns="http://www.w3.org/2000/svg" width="5.09ex" height="8.597ex" role="img" focusable="false" viewBox="0 -2150 2250 3800" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-27-TEX-S4-239B" d="M837 1154Q843 1148 843 1145Q843 1141 818 1106T753 1002T667 841T574 604T494 299Q417 -84 417 -609Q417 -641 416 -647T411 -654Q409 -655 366 -655Q299 -655 297 -654Q292 -652 292 -643T291 -583Q293 -400 304 -242T347 110T432 470T574 813T785 1136Q787 1139 790 1142T794 1147T796 1150T799 1152T802 1153T807 1154T813 1154H819H837Z"></path><path id="MJX-27-TEX-S4-239D" d="M843 -635Q843 -638 837 -644H820Q801 -644 800 -643Q792 -635 785 -626Q684 -503 605 -363T473 -75T385 216T330 518T302 809T291 1093Q291 1144 291 1153T296 1164Q298 1165 366 1165Q409 1165 411 1164Q415 1163 416 1157T417 1119Q417 529 517 109T833 -617Q843 -631 843 -635Z"></path><path id="MJX-27-TEX-S4-239C" d="M413 -9Q412 -9 407 -9T388 -10T354 -10Q300 -10 297 -9Q294 -8 293 -5Q291 5 291 127V300Q291 602 292 605L296 609Q298 610 366 610Q382 610 392 610T407 610T412 609Q416 609 416 592T417 473V127Q417 -9 413 -9Z"></path><path id="MJX-27-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-27-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-27-TEX-S4-239E" d="M31 1143Q31 1154 49 1154H59Q72 1154 75 1152T89 1136Q190 1013 269 873T401 585T489 294T544 -8T572 -299T583 -583Q583 -634 583 -643T577 -654Q575 -655 508 -655Q465 -655 463 -654Q459 -653 458 -647T457 -609Q457 -58 371 340T100 1037Q87 1059 61 1098T31 1143Z"></path><path id="MJX-27-TEX-S4-23A0" d="M56 -644H50Q31 -644 31 -635Q31 -632 37 -622Q69 -579 100 -527Q286 -228 371 170T457 1119Q457 1161 462 1164Q464 1165 520 1165Q575 1165 577 1164Q582 1162 582 1153T583 1093Q581 910 570 752T527 400T442 40T300 -303T89 -626Q78 -640 75 -642T61 -644H56Z"></path><path id="MJX-27-TEX-S4-239F" d="M579 -9Q578 -9 573 -9T554 -10T520 -10Q466 -10 463 -9Q460 -8 459 -5Q457 5 457 127V300Q457 602 458 605L462 609Q464 610 532 610Q548 610 558 610T573 610T578 609Q582 609 582 592T583 473V127Q583 -9 579 -9Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mrow"><g data-mml-node="mo"><use data-c="239B" xlink:href="#MJX-27-TEX-S4-239B" transform="translate(0,996)"></use><use data-c="239D" xlink:href="#MJX-27-TEX-S4-239D" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239C" xlink:href="#MJX-27-TEX-S4-239C" transform="scale(1,0.924)"></use></svg></g><g data-mml-node="mtable" transform="translate(875,0)"><g data-mml-node="mtr" transform="translate(0,1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-27-TEX-N-31"></use></g></g></g><g data-mml-node="mtr"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-27-TEX-N-31"></use></g></g></g><g data-mml-node="mtr" transform="translate(0,-1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="30" xlink:href="#MJX-27-TEX-N-30"></use></g></g></g></g><g data-mml-node="mo" transform="translate(1375,0)"><use data-c="239E" xlink:href="#MJX-27-TEX-S4-239E" transform="translate(0,996)"></use><use data-c="23A0" xlink:href="#MJX-27-TEX-S4-23A0" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239F" xlink:href="#MJX-27-TEX-S4-239F" transform="scale(1,0.924)"></use></svg></g></g></g></g></svg></mjx-container> und <mjx-container class="MathJax" jax="SVG"><svg alt="\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right)" style="vertical-align: -3.733ex;" xmlns="http://www.w3.org/2000/svg" width="5.09ex" height="8.597ex" role="img" focusable="false" viewBox="0 -2150 2250 3800" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-28-TEX-S4-239B" d="M837 1154Q843 1148 843 1145Q843 1141 818 1106T753 1002T667 841T574 604T494 299Q417 -84 417 -609Q417 -641 416 -647T411 -654Q409 -655 366 -655Q299 -655 297 -654Q292 -652 292 -643T291 -583Q293 -400 304 -242T347 110T432 470T574 813T785 1136Q787 1139 790 1142T794 1147T796 1150T799 1152T802 1153T807 1154T813 1154H819H837Z"></path><path id="MJX-28-TEX-S4-239D" d="M843 -635Q843 -638 837 -644H820Q801 -644 800 -643Q792 -635 785 -626Q684 -503 605 -363T473 -75T385 216T330 518T302 809T291 1093Q291 1144 291 1153T296 1164Q298 1165 366 1165Q409 1165 411 1164Q415 1163 416 1157T417 1119Q417 529 517 109T833 -617Q843 -631 843 -635Z"></path><path id="MJX-28-TEX-S4-239C" d="M413 -9Q412 -9 407 -9T388 -10T354 -10Q300 -10 297 -9Q294 -8 293 -5Q291 5 291 127V300Q291 602 292 605L296 609Q298 610 366 610Q382 610 392 610T407 610T412 609Q416 609 416 592T417 473V127Q417 -9 413 -9Z"></path><path id="MJX-28-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-28-TEX-S4-239E" d="M31 1143Q31 1154 49 1154H59Q72 1154 75 1152T89 1136Q190 1013 269 873T401 585T489 294T544 -8T572 -299T583 -583Q583 -634 583 -643T577 -654Q575 -655 508 -655Q465 -655 463 -654Q459 -653 458 -647T457 -609Q457 -58 371 340T100 1037Q87 1059 61 1098T31 1143Z"></path><path id="MJX-28-TEX-S4-23A0" d="M56 -644H50Q31 -644 31 -635Q31 -632 37 -622Q69 -579 100 -527Q286 -228 371 170T457 1119Q457 1161 462 1164Q464 1165 520 1165Q575 1165 577 1164Q582 1162 582 1153T583 1093Q581 910 570 752T527 400T442 40T300 -303T89 -626Q78 -640 75 -642T61 -644H56Z"></path><path id="MJX-28-TEX-S4-239F" d="M579 -9Q578 -9 573 -9T554 -10T520 -10Q466 -10 463 -9Q460 -8 459 -5Q457 5 457 127V300Q457 602 458 605L462 609Q464 610 532 610Q548 610 558 610T573 610T578 609Q582 609 582 592T583 473V127Q583 -9 579 -9Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mrow"><g data-mml-node="mo"><use data-c="239B" xlink:href="#MJX-28-TEX-S4-239B" transform="translate(0,996)"></use><use data-c="239D" xlink:href="#MJX-28-TEX-S4-239D" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239C" xlink:href="#MJX-28-TEX-S4-239C" transform="scale(1,0.924)"></use></svg></g><g data-mml-node="mtable" transform="translate(875,0)"><g data-mml-node="mtr" transform="translate(0,1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-28-TEX-N-31"></use></g></g></g><g data-mml-node="mtr"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-28-TEX-N-31"></use></g></g></g><g data-mml-node="mtr" transform="translate(0,-1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-28-TEX-N-31"></use></g></g></g></g><g data-mml-node="mo" transform="translate(1375,0)"><use data-c="239E" xlink:href="#MJX-28-TEX-S4-239E" transform="translate(0,996)"></use><use data-c="23A0" xlink:href="#MJX-28-TEX-S4-23A0" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239F" xlink:href="#MJX-28-TEX-S4-239F" transform="scale(1,0.924)"></use></svg></g></g></g></g></svg></mjx-container> aufgespannten Parallelogramms.</p>

<p>Berechne den Vektor $\left(\begin{array}{l}1 \\ 1 \\ 0\end{array}\right) \times\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right)$.</p>
<p> </p>
<p>Bestimme anschließend seine Länge und interpretiere sie.</p>

<p>Berechne den Vektor <mjx-container class="MathJax" jax="SVG"><svg alt="\left(\begin{array}{l}1 \\ 1 \\ 0\end{array}\right) \times\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right)" style="vertical-align: -3.733ex;" xmlns="http://www.w3.org/2000/svg" width="12.947ex" height="8.597ex" role="img" focusable="false" viewBox="0 -2150 5722.4 3800" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-23-TEX-S4-239B" d="M837 1154Q843 1148 843 1145Q843 1141 818 1106T753 1002T667 841T574 604T494 299Q417 -84 417 -609Q417 -641 416 -647T411 -654Q409 -655 366 -655Q299 -655 297 -654Q292 -652 292 -643T291 -583Q293 -400 304 -242T347 110T432 470T574 813T785 1136Q787 1139 790 1142T794 1147T796 1150T799 1152T802 1153T807 1154T813 1154H819H837Z"></path><path id="MJX-23-TEX-S4-239D" d="M843 -635Q843 -638 837 -644H820Q801 -644 800 -643Q792 -635 785 -626Q684 -503 605 -363T473 -75T385 216T330 518T302 809T291 1093Q291 1144 291 1153T296 1164Q298 1165 366 1165Q409 1165 411 1164Q415 1163 416 1157T417 1119Q417 529 517 109T833 -617Q843 -631 843 -635Z"></path><path id="MJX-23-TEX-S4-239C" d="M413 -9Q412 -9 407 -9T388 -10T354 -10Q300 -10 297 -9Q294 -8 293 -5Q291 5 291 127V300Q291 602 292 605L296 609Q298 610 366 610Q382 610 392 610T407 610T412 609Q416 609 416 592T417 473V127Q417 -9 413 -9Z"></path><path id="MJX-23-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-23-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-23-TEX-S4-239E" d="M31 1143Q31 1154 49 1154H59Q72 1154 75 1152T89 1136Q190 1013 269 873T401 585T489 294T544 -8T572 -299T583 -583Q583 -634 583 -643T577 -654Q575 -655 508 -655Q465 -655 463 -654Q459 -653 458 -647T457 -609Q457 -58 371 340T100 1037Q87 1059 61 1098T31 1143Z"></path><path id="MJX-23-TEX-S4-23A0" d="M56 -644H50Q31 -644 31 -635Q31 -632 37 -622Q69 -579 100 -527Q286 -228 371 170T457 1119Q457 1161 462 1164Q464 1165 520 1165Q575 1165 577 1164Q582 1162 582 1153T583 1093Q581 910 570 752T527 400T442 40T300 -303T89 -626Q78 -640 75 -642T61 -644H56Z"></path><path id="MJX-23-TEX-S4-239F" d="M579 -9Q578 -9 573 -9T554 -10T520 -10Q466 -10 463 -9Q460 -8 459 -5Q457 5 457 127V300Q457 602 458 605L462 609Q464 610 532 610Q548 610 558 610T573 610T578 609Q582 609 582 592T583 473V127Q583 -9 579 -9Z"></path><path id="MJX-23-TEX-N-D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mrow"><g data-mml-node="mo"><use data-c="239B" xlink:href="#MJX-23-TEX-S4-239B" transform="translate(0,996)"></use><use data-c="239D" xlink:href="#MJX-23-TEX-S4-239D" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239C" xlink:href="#MJX-23-TEX-S4-239C" transform="scale(1,0.924)"></use></svg></g><g data-mml-node="mtable" transform="translate(875,0)"><g data-mml-node="mtr" transform="translate(0,1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-23-TEX-N-31"></use></g></g></g><g data-mml-node="mtr"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-23-TEX-N-31"></use></g></g></g><g data-mml-node="mtr" transform="translate(0,-1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="30" xlink:href="#MJX-23-TEX-N-30"></use></g></g></g></g><g data-mml-node="mo" transform="translate(1375,0)"><use data-c="239E" xlink:href="#MJX-23-TEX-S4-239E" transform="translate(0,996)"></use><use data-c="23A0" xlink:href="#MJX-23-TEX-S4-23A0" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239F" xlink:href="#MJX-23-TEX-S4-239F" transform="scale(1,0.924)"></use></svg></g></g><g data-mml-node="mo" transform="translate(2472.2,0)"><use data-c="D7" xlink:href="#MJX-23-TEX-N-D7"></use></g><g data-mml-node="mrow" transform="translate(3472.4,0)"><g data-mml-node="mo"><use data-c="239B" xlink:href="#MJX-23-TEX-S4-239B" transform="translate(0,996)"></use><use data-c="239D" xlink:href="#MJX-23-TEX-S4-239D" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239C" xlink:href="#MJX-23-TEX-S4-239C" transform="scale(1,0.924)"></use></svg></g><g data-mml-node="mtable" transform="translate(875,0)"><g data-mml-node="mtr" transform="translate(0,1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-23-TEX-N-31"></use></g></g></g><g data-mml-node="mtr"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-23-TEX-N-31"></use></g></g></g><g data-mml-node="mtr" transform="translate(0,-1400)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-23-TEX-N-31"></use></g></g></g></g><g data-mml-node="mo" transform="translate(1375,0)"><use data-c="239E" xlink:href="#MJX-23-TEX-S4-239E" transform="translate(0,996)"></use><use data-c="23A0" xlink:href="#MJX-23-TEX-S4-23A0" transform="translate(0,-1006)"></use><svg width="875" height="382" y="59" x="0" viewBox="0 86.3 875 382"><use data-c="239F" xlink:href="#MJX-23-TEX-S4-239F" transform="scale(1,0.924)"></use></svg></g></g></g></g></svg></mjx-container>.</p>
<p> </p>
<p>Bestimme anschließend seine Länge und interpretiere sie.</p>

Dies ist eine interaktive Aufgabe zu: Winkel, Länge, Fläche, Volumen von Vektoren mit praktischen Tipps zum Lösen und einer Zusammenfassung der nötigen Theorie

Vektorrechnung - Winkel, Länge, Fläche, Volumen von Vektoren | Aufgabe

Aufgabenstellung:

Lösungsweg:

Lösung: