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 (this means $a \cdot b =0)$.
(b) Projection of $b$ on $a$ is equal to that of $a$ on $b$ if $a =b$ or the two vectors are orthogonal ($a \cdot b =0$).
Work Step by Step
(a) $comp_ab=comp_ba$ when $\frac {a \cdot b}{|a|}=\frac {a \cdot b}{|b|}$
$comp_ab=comp_ba$ for $|a| = |b|$
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) $proj_ab=proj_ba$ when $\frac {a \cdot b}{(|a|)^2} \cdot a=\frac {a \cdot b}{(|b|)^2} \cdot b$
$comp_ab=comp_ba$ which happens only if $a=b$
Projection of $b$ on $a$ is equal to that of $a$ on $b$ if $a =b$ or the two vectors are orthogonal.
