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See this statement: $$ |u×v|^2=|u|^2\cdot|v|^2-(u\cdot v)^2 $$

I need to prove this is right.

I only found that: $$ u×v=|u|\cdot|v|\cdot\sin\theta $$ and $$ u.v=|u|\cdot|v|\cdot\cos\theta $$

Does this helps?

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