Calculus Projection

Question

Let a=<0,4,−4> and b=<−1,−3,−2>.

Find the projection of b onto a 

Answer 1

a.b * a/|a|² = (0, 4, -4) . (-1, -3, -2) * (0, 4, -4) / (0² + 4² + (-4)²) =

-4(0, 4, -4)/32 =

(0, -1/2, 1/2)

Note that b - (0, -1/2, 1/2) = (-1, -3, -2) - (0, -1/2, 1/2) = (-1, - 5/2, -5/2), and (-1, - 5/2, -5/2) . (0, 4, -4) = 0, a check that the work is correct.