Question

The vector A = (2x + 3y) m and the sum A+B has a magnitude of 4 m oriented at 120 degrees from the x axis. Calculate the magnitude and orientation of the B vector.

Answer 1

Find the x- and y-components of the sum R=(A+B):

$$A_x=2,\\ A_y=3,\\ B_x=R\cos\theta-A_x=4·\cos120°-2=-4\text{ m},\\ B_y=R\sin\theta-A_y=0.464\text{ m},\\\space\\ B=\sqrt{B_x^2+B_y^2}=4.03\text{ m},\\\space\\ \theta=180°-\arctan\frac{|B_y|}{|B_x|} =173°$$

from the x-axis.