Let u = 6i + 5j and v = 4i − j.

Question

Let u = 6i + 5j and v = 4i − j.

(a) Find the angle between u and v. (Round your answer to one decimal place.)

 °

(b) Find the component of u along v.

 

(c) Find proj_vu.

Answer 1

(a) cosθ = u•v/(IuI·IvI) = (6·4 + 5(- 1))/(√36 + 25·√16 + 1) = 19/√61·17 = 19/√1037;

θ = cos^-1(19/√1037) = 53.84°.

(b) comp_vu = IuIcosθ = √61·19/(√61·√17) = 19/√17

(c) proj_vu = 19/√17·v/IvI = (19/√17)·(4i - j)/√17 = 10/17(4i - j) = 76/17i - 19/17j