Question

Find the direction angle of the vector below. Round to the nearest thousandth. Show all work.

Answer 1

For a vector given in the form:

`v=ai+bj`

the direction angle of the vector is given to be:

`\theta=\tan ^(-1)((b)/(a))`

The vector is given in the question to be:

`v=3i+4j`

Therefore, we have that:

`\begin{gathered} a=3 \\ b=4 \end{gathered}`

Hence, the direction angle is calculated to be:

`\begin{gathered} \theta=\tan ^(-1)((4)/(3)) \\ \theta=53.130\degree \end{gathered}`

The direction angle is 53.130° to the nearest thousandth.