Question: If vector $a = <2,3,5>$ and vector $b = <2,-2,-1>$, find the vector projection of b onto a and hence find the component of b perpendicular to a.
I found the vector projection of b onto a using the vector projection formula which is (-7/38)<2,3,5>.
Do I find the component of b perpendicular to a by using vector b - vector projection? Would this be <2,-2,-1> - (-7/38)<2,3,5>?
Vector Projection = $\mbox{proj}_{a}b=\dfrac{a\cdot b}{|a|^2}a=\dfrac{\langle2,3,5\rangle\langle2,-2,-1\rangle}{38}(2)$
The component of b perpendicular to a is $b-\mbox{proj}_{a}b$