Prove that cross product of two vectors is equal to the area of a parallelogram

Answers (1)

Let \ \ a$ and $b$ be two vectors.\\ $a \times b=|a||b| \sin (\theta) \quad$ \\where\\ $|a|=$ magnitude of $a$\\ IbI = magnitude of b\\ $\theta=$ angle between $\mathrm{a}$ and $\mathrm{a}$

If you draw a parallelogram with sides as vector a and b As shown below

then The area of the parallelogram will be Area= |\vec{a}|\times h

where h is the perpendicular height 

And h is given as h=bsin\theta

\text { So area }=|a| h=|a||b| \sin (\theta)=\vec{a}\times \vec{b}

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