math Question!!!

Question

You are given the 2D vectors X = {-3, 5}, and Y = {2, -2}.a) If the tails of X and Y are at the origin, what is the distance from the tip of X to the tip of Y?

What is YcompX, the component vector of Y in the direction of X

Answer 1

a) Distance d = √(-3 - 2)² + (5 + 2)² = √74;

b)X = {-3, 5}, and Y = {2, -2}

Component Y on the direction of X this is projection Y on X: proj_XY = IYI·(X·Y)X/[IXI·IYI·IXI = (X·Y)X/IXI² =

(- 6 - 10){-3, 5}/(9 + 25) = {24/17, - 40/17}