Question

Find the direction angle of v for the following vector.

Answer 1

To solve this problem, we will use the following formula for the direction angle of a vector x=ai+bj:

`\tan \theta=((b)/(a)).`

In the given problem:

`\begin{gathered} a=-8\sqrt[]{3}, \\ b=8. \end{gathered}`

Therefore:

`tan\theta=(\frac{8}{-8\sqrt[]{3}})\text{.}`

Simplifying the above result, we get:

`\tan \theta=(-\frac{1}{\sqrt[]{3}}).`

Therefore, since the vector is in the second quadrant, we get:

`\theta=150^(\circ).`

Answer:

`150^(\circ).`