Question

Which of the following is the direction angle of a vector that has initial point is (-4, -1) and terminalpoint is (10, -7)? Round your answer to the nearest hundredth of a degree.

Answer 1

We have a vector with initial point (-4,-1) and terminal point (10,-7).

We have to find its direction angle α. This can be related to the points as:

Then, we use the trigonometric ratio:

$\tan (\alpha)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{-6}{14}=-\frac{3}{7}$

And the angle is:

$\alpha=\arctan (-\frac{3}{7})\approx-23.19\degree$

Answer: 23.19° (the dire