Chapter 9.1, Problem 51E

To determine

To find: The magnitude and direction of given vector.

Answer to Problem 51E

The magnitude and direction of given vector is $2$ and $60°$ respectively.

Explanation of Solution

Given information:

The vector is $v=i+\sqrt{3}j$ .

Calculation:

The magnitude of vector is,

  $\begin{array}{c}\left|v\right|=\sqrt{{\left(a\right)}^2+{\left(b\right)}^2}\\ =\sqrt{{\left(1\right)}^2+{\left(\sqrt{3}\right)}^2}\\ =\sqrt{1+3}\\ =2\end{array}$

The direction of vector is,

  $\begin{array}{c}\theta ={\tan }^{-1}\left(\frac{b}{a}\right)\\ ={\tan }^{-1}\left(\frac{\sqrt{3}}{1}\right)\\ =60°\end{array}$