Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in $$\left[ 0,360 ^ { \circ } \right]$$
-$\langle - 12,5 \rangle$
A) $13 ; 112.6 ^ { \circ }$
B) $13 ; 157.4 ^ { \circ }$
C) $15 ; 157.4 ^ { \circ }$
D) $13 ; 22.6 ^ { \circ }$

Question

Quizplus · Accepted Answer

The magnitude of the vector $\langle -12, 5 \rangle$ is calculated using the formula $\sqrt{(-12)^2 + 5^2} = 13$. The direction angle is found using $\tan^{-1}(\frac{5}{-12})$, which gives an angle in the fourth quadrant. Adjusting to the correct quadrant, the angle is $157.4^\circ$.

Find the Magnitude and Direction Angle (To the Nearest Tenth) [0,360∘]\left[ 0,360 ^ { \circ } \right][0,360∘]

Find the Magnitude and Direction Angle (To the Nearest Tenth) $\left[ 0,360 ^ { \circ } \right]$