Question

Can someone answer this, please and thanks? Vector A points in the negative y direction and has a magnitude of 11 units. Vector B has twice the magnitude and points in the positive x direction. Find the direction and magnitude of A + B.

Answer 1

\[A+B=(A _{x}+B _{x})i+(A _{y}+B _{y})j\] From the problem we get

\[(0+22)i+(-11+0)j=22i-11j\] For the direction of a two dimensional vector we can get the formula \[\theta = \arctan(y/x)\] which comes from trigonometry. So you compute that and make sure to pay attention the signs on the x and y terms to determine which quadrant it is in.