Question

Vector A is 3.0 units in length and points along the positive x-axis; vector B is 4.0 units in length and points along a direction 150 from the positive x-axis. What is the magnitude of the resultant when vectors A and B are added?

Answer 1

Find the x- and y-components of both vectors, then find the x- and y-components of the resultant, then find the magnitude of the resultant itself:

$$A_x=3,\\ A_y=0.\\ B_x=B\cos\theta=4\cos150°=-3.46,\\ B_y=B\sin\theta=4\sin150°=2.\\\space\\ R_x=A_x+B_x,\\ R_y=A_y+B_y,\\ R=\sqrt{R_x^2+R_y^2}=2.05.$$