Chapter 6, Problem 71RE

To determine

To find: The angle between the vectors.

Answer to Problem 71RE

The angle between the vectors is $15.05°$ .

Explanation of Solution

Given information:

The given vectorsare,

  $\begin{array}{l}u=\cos \frac{7\pi }{4}i+\sin \frac{7\pi }{4}j\\ v=\cos \frac{5\pi }{6}i+\sin \frac{5\pi }{6}j\end{array}$

Concept used:

The angle between the two vectors is calculated as,

  $\cos \theta =\frac{u\cdot v}{\Vert u\Vert \Vert v\Vert }$

The angle between the two vectors is calculated as,

  $\begin{array}{l}\cos \theta =\frac{u\cdot v}{\Vert u\Vert \Vert v\Vert }\\ \cos \theta =\frac{\langle \cos \frac{7\pi }{4},\sin \frac{7\pi }{4}\rangle \cdot \langle \cos \frac{5\pi }{6},\sin \frac{5\pi }{6}\rangle }{\Vert \langle \cos \frac{7\pi }{4},\sin \frac{7\pi }{4}\rangle \Vert \Vert \langle \cos \frac{5\pi }{6},\sin \frac{5\pi }{6}\rangle \Vert }\\ \cos \theta =\frac{\langle 0.707,-0.707\rangle \cdot \langle -0.866,0.5\rangle }{\Vert \langle 0.707,-0.707\rangle \Vert \Vert \langle -0.866,0.5\rangle \Vert }\\ \cos \theta =\frac{0.9657}{\left[1\right]\left[1\right]}\end{array}$

Simplify further,

  $\theta =15.05°$

Therefore, the angle between the vectorsis $15.05°$ .