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WZ
Numerade Educator

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Problem 48 Medium Difficulty

Suppose that $ a $ and $ b $ are nonzero vectors.
(a) Under what circumstances is $ comp_a b = comp_b a $?
(b) Under what circumstances is $ proj_a b = proj_b a $?

Answer

a) The scalar projection of $b$ onto $a$ is equal to the scalar projection of $a$ onto $b$ when the length of $a$ is equal to the length of $b$ or when $a$ and $b$ are orthogonal.
b) Projection of $\vec{b}$ on $\vec{a}$ is equal to that of $\vec{a}$ on $\vec{b}$ If
$\vec{a}=\vec{b}$
OR The two vectors are orthogonal

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Video Transcript

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