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