Question

Determine the projection of u=1.6i+3.3j in the v=-2.1-.5j direction.

A.8i+.2j

B.2.3i+.5j

C. -.6i-1.3j

D. -1.2i-1.1j

Answer 1

`0.80i +0.2j`

Explanation:

The projection of u on v is expressed as;

`proj_(v) u = (u*v)/(|v|^2) * v`

Given

u=1.6i+3.3j

v=-2.1i-.5j

u*v = (1.6i+3.3j )*(-2.1i-0.5j )

u*v = 1.6i(-2.1i) + 3.3j(-0.5j)

u*v = -3.36 - 1.65

u*v = -5.01

|v|² = (√(-2.1)²+(-0.5)²)²

|v|² = (-2.1)²+(-0.5)²

|v|² = 4.41+0.25

|v|² = 4.66

Substitute into the formula;

`= (1.71)/(-5.01) * (-2.1i - 0.5j)\\= -0.3413 (-2.1i - 0.5j)\\= 0.8i + 0.17j\\= 0.80i +0.2j`