Given vectors V and W, we wish to write V as the sum of a) a vector parallel to W; b) a vector perpendicular to W.
Summary: Given V and W (W had better not be 0) the vector perp. = V - (VW/WW)W has the two properties (1) perp. is perpendicular to W, and (2) (perp.) + (proj. of V on W) = V.