Resolving a vector into a sum of two vectors

"Resolve the vector **u** = 5**i** + **j** + 6**k** into a sum of two vectors, one of which is parallel and the other perpendicular to **v** = 3**i** - 6**j** + 2**k**."

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.