Three vectors have the following x and y components:
The angle that the resultant makes with the positive direction of the x axis is
A) 1.2º
B) 36º
C) 50º
D) 40º
E) 70º

Question

Three vectors   have the following x and y components:  
The angle that the resultant makes with the positive direction of the x axis is
A) 1.2º 
B) 36º 
C) 50º 
D) 40º 
E) 70º

Quizplus · Accepted Answer

First, we need to find the x and y components of the resultant vector by adding the x and y components of the three given vectors:
x component:
11*cos(20°) + 11*cos(45°) + 11*cos(60°) = 8.82 + 7.78 + 5.5 = 22.1
y component:
11*sin(20°) + 11*sin(45°) + 11*sin(60°) = 3.8 + 7.78 + 9.55 = 21.13

The magnitude of the resultant vector is:
|r| = sqrt((22.1)^2 + (21.13)^2) = 30.25

The angle that the resultant vector makes with the positive direction of the x-axis is:
theta = arctan(21.13/22.1) = 48.4°

Therefore, the closest option is C) 50º.

Three Vectors Have the Following X and Y