Chapter 6, Problem 73RE

To determine

To Find: find the magnitude and direction angle of the vector v.

Answer to Problem 73RE

  $\begin{array}{l}\left|v\right|=4.24\\ Direction=Q={45}^{°}\end{array}$

Explanation of Solution

Given information:

  $v=-3i-3j$

Formula used:

  $v=ai+bj$

Magnitude= $\left|v\right|=\sqrt{a^2+b^2}$

Direction= $Q={\tan }^{-1}\frac{b}{a}$

Calculation:

  $\begin{array}{l}v=-3i-3j\\ \left|v\right|=\sqrt{{(-3)}^2+{(-3)}^2}\\ \left|v\right|=\sqrt{9+9}\\ \left|v\right|=\sqrt{18}\end{array}$

  $\left|v\right|=4.24$

  $\begin{array}{l}Direction=Q={\tan }^{-1}\left(\frac{-3}{-3}\right)={\tan }^{-1}1\\ \boxed{Q={45}^{°}}\end{array}$