Chapter 9.4, Problem 59AYU

To determine

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

Answer to Problem 59AYU

Solution:

$-7i+7\sqrt{3}j$

Explanation of Solution

Given:

$\Vert v\Vert =14,\alpha =120°$ with the positive $x\text{-axis}$.

Calculation:

The magnitude of $v$ is $\Vert v\Vert =14$, and the angle between the direction of $v$ and $i$, the positive $x\text{-axis}$, is $\alpha =120°$.

$v=\Vert v\Vert \left(\cos \alpha i+\sin \alpha j\right)=14\left(\cos 120°i+\sin 120°j\right)=14\left(-\frac{1}{2}i+\frac{\sqrt{3}}{2}j\right)=-7i+7\sqrt{3}j$