Vector A is directed along the positive y-axis and has a magnitude of sqrt 3.0 units. Vector B is directed along the negative x-axis and has magnitude 1.0 units. What are the magnitude and direction of A + B?

Question

Vector A is directed along the positive y-axis and has a magnitude of sqrt 3.0 units.  Vector B is directed along the negative x-axis and has magnitude 1.0 units.  What are the magnitude and direction of A + B?

drwls · Accepted Answer

Since A and B are perpendicular, use the Pythagorean theorem for the magnitude. Mag = sqrt[(sqrt3)^2+1] = sqrt 4 = 2 The sum vector A + B is arctan 1/sqrt3 = 30 degrees west of north.

Dakota · Answer

Thank you. Could you explain to me why we use arctan?? I just want to have a better understanding of why?

Tammy J · Answer

Vector A is directed along the positive y-axis and has magnitude sqrt 3.0 units. Vector B is directed along the negative x-axis and has a magnitude 1.0 units. (a) what are the magnitude and direction of A-B? (b) what are the x and y components of B-A?