How Is the Magnitude of the Cross Product Related to Parallelogram Area?

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Start date Mar 1, 2010
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Area Cross Cross product Product

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The magnitude of the cross product ||V x U|| represents the area of the parallelogram formed by vectors V and U. This relationship is established through geometric interpretation, where the area is calculated as the product of the base and height, with the height being represented by the sine of the angle between the two vectors. The cross product yields a vector perpendicular to both V and U, reinforcing this area calculation. A proof was found that confirms this concept. Understanding this relationship is crucial in vector calculus and physics applications.

Mar 1, 2010

ƒ(x)

How do you prove that ||VxU|| is the area of the parallelegram they form?

I know that the cross product is a vector perpendicular to V and U

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Mar 1, 2010

ƒ(x)

Nvm, found a proof.

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