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:

$\theta=\tan ^{-1}(\frac{b}{a})$

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:

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

The direction angle is 53.130° to the nearest thousandth.