If $a\cdot b = 0$ and $x+ (x\cdot b)\,a = b$, find the vector $x$.
I don’t know how to approach this question. I understand that $x\cdot b$ will be a scalar - but is it cross producted to $a$? Any hints or a walkthrough with this question would be greatly appreciated.
Hint. Take dot products on both sides with $b$. This allows you to determine the value of $x\cdot b$ in terms of $a$ and $b$. Once you have done this, the answer is given by $x=b-(x\cdot b)a$.