Question

Determine the projection of u = 1.6i + 3.3j in the v = -2.1i - 0.5j direction

a. 0.8i +0.2j
b. 2.3i = 0.5j
c.-0.6i-1.3j
d. -1.2i-1.1j

Answer 1

To find the angle between u and v,

|u|*|v| cosθ = u•v
3.67*2.16 cosθ = (1.6)(-2.1)+(3.3)(-0.5)
cosθ = -5.01/7.93 = -0.63
θ = 129.18°

So the projection of u on v is

|u|cosθ v/|v|
= 3.67(-0.63)/2.16 v
= -1.07v
≈ 2.3i+0.5j

Answer 2

or, without finding the angle,

projection of u on v
= (u dot v)/|v|^2 * v
= (1.6*-2.1 + 3.3*-.5)/√(4.41+.25)^2 * v
= appr -1.0796 v
= appr 2.26i + .539j ----> given as choice b), same as Steve's answer