Suppose that the sum of the three vectors u v and w shown in

Suppose that the sum of the three vectors u, v, and w shown in the figure is the zero vector. If |w| = 35, find |u| and |v|. Carry your intermediate computations to at least 4 decimal places. Round your answers to the nearest tenth.

Solution

writing the equations for x and y component

x component equation is

u cos 33 - v cos 16 + w cos 53 = 0

plugging the values of each angle

.8386u - .9612v + 21.06 = 0

y component equation

- u sin 33 + v sin 16 + w sin 53 = 0

-.5446u +.2756v + 27.95 = 0

solving the two equations for u and v

on solving we get

u = 111.74

v = 119.40