Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0°, 360°) rounded to the nearest tenth.
-$- 7 i + 2 j$
A) $\sqrt { 53 } , 164.1 ^ { \circ }$
B) $9,344.1 ^ { \circ }$
C) $\sqrt { 53 } , 15.9 ^ { \circ }$
D) $53,164.1 ^ { \circ }$

Question

Quizplus · Accepted Answer

The magnitude of the vector $-7i + 2j$ is $\sqrt{(-7)^2 + 2^2} = \sqrt{49 + 4} = \sqrt{53}$. The direction angle, measured counterclockwise from the positive x-axis, is given by $\tan^{-1}\left(\frac{2}{-7}\right)$, which is in the second quadrant, leading to an angle of approximately $164.1^\circ$.

Find the Magnitude and Direction Angle for the Following Vector −7i+2j- 7 i + 2 j−7i+2j

Find the Magnitude and Direction Angle for the Following Vector $- 7 i + 2 j$