Write the vector $u = (5,1,5)$ as the sum of two vectors, $v$ and $w$, such that $v \| p = (1,1,0)$ and $v ⊥ w$.
So what I did was let $v=(1,1,0)$ and $w = (5-1,1-1,5-0)$ Which is obviously wrong because i'm not using the cross product what so ever. So my assumption of $v$ must be wrong. Why is this? Or am I reading the question wrong?