Chapter 9.4, Problem 58AYU

To determine

To write: The vector $v$ in the form $ai + bj$.

Answer to Problem 58AYU

Solution:

$4\sqrt{2}i+4\sqrt{2}j$

Explanation of Solution

Given:

$\Vert v\Vert =8, \alpha =45°$ with the positive $x\text{-axis}$.

Calculation:

The magnitude of $v$ is $\Vert v\Vert = 8$, and the angle between the direction of $v$ and $i$, the positive $x\text{-axis}$, is $\alpha = 45°$.

$v=\Vert v\Vert \left(\text{cos}\alpha i+\text{sin}\alpha j\right)=8\left(\text{cos}45°i+\text{sin}45°j\right)=8\left(\frac{\sqrt{2}}{2}i+\frac{\sqrt{2}}{2}j\right)=4\sqrt{2}i+4\sqrt{2}j$