Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].
--12, 5
A)13; 157.4°
B)15; 157.4°
C)13; 22.6°
D)13; 112.6°

Question

Quizplus · Accepted Answer

The magnitude of the vector is calculated using the formula $\sqrt{(-12)^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13$. The direction angle $\theta$ can be found using the tangent function $\tan(\theta) = \frac{5}{-12}$, which gives $\theta \approx 157.4°$ when adjusted to the [0,360°] range, considering the vector is in the second quadrant.

Find the Magnitude and Direction Angle (To the Nearest Tenth)