Given the vectors v and w, write v = v∥ + vp, where v∥ is parallel to w, and vp is perpendicular to w:
a) v = (2, 3, -7); w = (1,-2,-5)
b) v = (-3, 1, 2); w = (8,5,-3)
I found this in an old midterm and I'm not sure how to progress. I know that to find a perpendicular vector the dot product must be 0 and that a parallel vector a multiple of the vector. Any help is appreciated.