Q:

When projection of $a$ onto $b$ is equal to projection of $ b$ onto $a$

Having a lot of trouble with my Linear Algebra course and am stuck on this question. 
"Suppose $a$ and $b$ are non-zero vectors in $\mathbb R^n$ with the property that proj $a$ onto $b$ = proj $b$ onto $a$. What can you conclude about $a$
and $b$ $?$ Justify by describing the implied geometry and also by providing an
algebraic calculation that shows your intuition is correct."
Any help would be greatly appreciated

A:

Hint: projecting a vector onto $\bf v$ yields a vector parallel to $\bf v$.

