Cross Product

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Calc IV

Last updated 10:05 PM on 4/9/26
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Cross Product of u×v (box method)

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Cross Product u×v (formula method)

(u2v3-u3v2)i-(u1v3-u3v1)j+(u1v2-u2v1)k

<p>(u<sub>2</sub>v<sub>3</sub>-u<sub>3</sub>v<sub>2</sub>)i-(u<sub>1</sub>v<sub>3</sub>-u<sub>3</sub>v<sub>1</sub>)j+(u<sub>1</sub>v<sub>2</sub>-u<sub>2</sub>v<sub>1</sub>)k</p>
3
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Cross Product theorem 1

u and v are parallel if (theta/degree=0 or pi) u×v=0

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Cross Product theorem 2

The area of the parallelogram is |u×v|=|u||v|sin(theta/degree)

<p>The area of the parallelogram is |u×v|=|u||v|sin(theta/degree)</p>