Chapter 14, Problem 12CLR

To determine

To find the magnitude of $u-v$ to three significant digit and it’s bearing to nearest tenth of a degree.

Answer to Problem 12CLR

  $13.2$ , ${165}^{\circ }$ .

Explanation of Solution

Given:

The vector $u$ has magnitude $10$ and bearing ${200}^{\circ }$ and vector $v$ has magnitude $8$ and bearing ${35}^{\circ }$ .

Calculation:

The magnitude of $u-v$ is -

  $\begin{array}{l}\left|u-v\right|=\sqrt{u^2+v^2-2uv\cos \theta }\\ \left|u-v\right|=\sqrt{{10}^2+8^2-2(8)(10)\cos (200-35)}\\ =\sqrt{164-160\cos 165}\\ =\sqrt{174.6}\\ =13.2\end{array}$

And bearing

  $\begin{array}{l}$ {(200-35)}^{\circ }$={165}^{\circ }\end{array}$