Chapter 3.7, Problem 20P

Verify equations (7.13) using Figure 7.5. Hints: Write $r\text{'}=r$ as $i\text{'}x\text{'}+j\text{'}y\text{'}=ix+jy$ and take the dot product of this equation with $i\text{'}$ and with $j\text{'}$ to get $x\text{'}$ and $y\text{'}$.

Evaluate the dot products of the unit vectors in terms of $\theta$ using Figure 7.5. For example, $i\text{'}\cdot j$ is the cosine of the angle between the x' axis and the y axis.