Find the projection of u onto v.

Question

U = {3,6}

v = (4,6)

Options:

a. 13{72,48}

b. 1/13 {3,4}

c. 13/12 {48,72}

d. 1/13 {48,72}

e. 12/13 {48.72}

Answer 1

<u,v> means dot product of u and v

Orthogonal projection of u onto v is <u,v>/<v,v> times v.

<u,v> = 3*4 + 6² = 48 and <v,v> = 4² + 6² = 52, so <u,v>/<v,v> = 48/52 = 12/13. Therefore projection of u onto v is 12/13 * (4, 6). Answer d) is the right answer.