Let a 4 3 9 and b 110 4 be vectors Find the scalar vector

Let a = (4, -3, -9) and b = (1,10, -4) be vectors. Find the scalar, vector, and orthogonal projections of b onto a.

scalar projection (?)
Vector Projection ( , , )
Orthogonal Projection: ( , ,)

scalar b onto a = |b|cos(theta) = a.b / |a| = 10/sqrt(106) = .97 vector proj= scalar proj*vector = .97*(4,-3,-9) orthogonal proj = b-vector proj = (1,10,-4) - .97(4,-3,-9) = approx ( -3.12, 12.92 , 5.27)