Chapter 14.2, Problem 4ST

To determine

To find: The angle between the given vectors.

Answer to Problem 4ST

The angle in between is $\theta =42.4°$ .

Explanation of Solution

Given:

The given vector is $u=5i+2j$ and $v=8i-3j$ .

Calculation:

Consider $u=5i+2j$ and $v=8i-3j$ .

Then, the angle between them is,

  $\begin{array}{c}\cos \theta =\frac{u\cdot v}{\left|\left|u\right|\right|\left|\left|v\right|\right|}\\ =\frac{\langle 5,2\rangle \langle 8,3\rangle }{\sqrt{5^2+2^2}\sqrt{8^2+{\left(-3\right)}^2}}\\ =\frac{5\cdot 8+2\left(-3\right)}{\sqrt{29}\sqrt{73}}\\ =\frac{34}{\sqrt{2117}}\end{array}$

Then,

  $\begin{array}{c}\theta ={\cos }^{-1}\frac{34}{\sqrt{2117}}\\ =42.4°\end{array}$