Consider the vectors a=<2,4,-3> and b=<4,-5,6>. Determine vectors v and w such that a=v+w and v is parallel to b while w is orthogonal to b. The dot product of two orthogonal vectors is zero and the cross product of two parallel vectors is zero. A parallel vector is a multiple of the chosen vector. I tried using multiples of b for v and then seeing if random vectors orthogonal to b can be added to v to give a. I'm lost here.