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WZ
Numerade Educator

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Problem 65 Hard Difficulty

If $ \theta $ is the angle between vectors $ a $ and $ b $, show that
$$ proj_a b \cdot proj_b a = (a \cdot b) \cos^2 \theta $$

Answer

$\operatorname{Proj}_{\mathbf{a}} \mathbf{b} \cdot \operatorname{Proj}_{\mathbf{b}} \mathbf{a}=\frac{|\mathbf{b}| \cos \theta}{|\mathbf{a}|} \mathbf{a} \cdot \frac{|\mathbf{a}| \cos \theta}{|\mathbf{b}|} \mathbf{b}=\mathbf{a} \cdot \mathbf{b} \cos ^{2} \theta$

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Video Transcript

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