Resolving a vector into a sum of two vectors
"Resolve the vector u = 5i + j + 6k into a sum of two vectors, one of which is parallel and the other perpendicular to v = 3i - 6j + 2k."
What I want to know with this question is how you are able to know how to find the sum of each vector. I know that you find the vector projection of u in the direction of v and the vector component u orthogonal to v for the sum of two vectors. I know how to solve and find the answers from this so, I just basically want to know why you have to use these two in particular to get the answer.