Chapter 9.4, Problem 60AYU

To determine

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

Answer to Problem 60AYU

Solution:

$-\frac{3}{2}i-\frac{3\sqrt{3}}{2}j$

Explanation of Solution

Given:

$\Vert v\Vert =3,\alpha =240°$ with the positive $x\text{-axis}$.

Calculation:

The magnitude of $v$ is $\Vert v\Vert =3$, and the angle between the direction of $v$ and $i$, the positive $x\text{-axis}$, is $\alpha =240°$.

$v=\Vert v\Vert \left(\cos \alpha i+\sin \alpha j\right)=3\left(\cos 240°i+\sin 240°j\right)=3\left(-\frac{1}{2}i-\frac{\sqrt{3}}{2}j\right)=-\frac{3}{2}i-\frac{3\sqrt{3}}{2}j$