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

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

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