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}}=(-6)/(14)=-(3)/(7)`

And the angle is:

`\alpha=\arctan (-(3)/(7))\approx-23.19\degree`

Answer: 23.19° (the dire