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2 votes

Why is the magnitude of the cross product equal to the parallelogram spanned by the two vectors?

Regarding the second question: The formula for $|a\times b|$ follows from four axioms: $|a\times b| = |a||b|$ if $a\perp b$. $a\times a = 0$. Bilinearity of $\times$. $a\cdot b = |a||b|\cos\theta$. ...
Nicholas Todoroff's user avatar
3 votes

Why is the magnitude of the cross product equal to the parallelogram spanned by the two vectors?

Q1. What is the purpose of wanting the cross product to have magnitude equal to the parallelogram spanned by $a$ and $b$? I'm not sure what sort of answer you expect to get to this question. The ...
Blitzer's user avatar
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