Chapter 3, Problem 23PCE

An air traffic controller observes two airplanes approaching the airport. The displacement from the control tower to plane 1 is given by the vector $\stackrel{\to }{\text{A}}$, which has a magnitude of 220 km and points in a direction 32° north of west. The displacement from the control tower to plane 2 is given by the vector $\stackrel{\to }{\text{B}}$, which has a magnitude of 140 km and points 65° east of north. (a) Sketch the vectors $\stackrel{\to }{\text{A}}$, $-\stackrel{\to }{\text{B}}$, and $\stackrel{\to }{\text{D}}=\stackrel{\to }{\text{A}}-\stackrel{\to }{\text{B}}$. Notice that $\stackrel{\to }{\text{D}}$ is the displacement from plane 2 to plane 1. (b) Find the magnitude and direction of the vector $\stackrel{\to }{\text{D}}$.