# Determine the direction angle of the vector u= \left \langle -5, -7 \right \rangle.

## Question:

Determine the direction angle of the vector {eq}u= \left \langle -5, -7 \right \rangle. {/eq}

## Direction of a Vector:

The direction of the vectors is usually with respect to a horizontal axis, in a two-dimensional system this axis is the axis of the abscissa. The direction of a vector is found by applying the tangent of the angle, that is: {eq}\tan\theta=\frac{y}{x} {/eq}. The angle is: {eq}\theta=\tan^{-1}\left(\frac{y}{x}\right) {/eq}

The direction angle is given by: {eq}\theta=\tan^{-1}\left(\frac{y}{x}\right) {/eq}

{eq}\vec{u}=\left\langle -5,-7 \right\rangle {/eq}

Then,

{eq}\begin{align*} \theta&=\tan^{-1}\left(\frac{y}{x}\right) \\ \theta&=\tan^{-1}\left(\frac{-7}{-5}\right) \\ \theta&=\tan^{-1}\left(\frac{7}{5}\right) \\ \theta&=54.5^{\circ} \end{align*} {/eq}