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.
-$\langle 11,7 \rangle$
A) $\sqrt { 170 } , 32.5 ^ { \circ }$
B) $\sqrt { 170 } , 57.5 ^ { \circ }$
C) $\sqrt { 170 } , 212.5 ^ { \circ }$
D) $\sqrt { 170 } , 237.5 ^ { \circ }$

Question

Quizplus · Accepted Answer

The magnitude of the vector $\langle 11,7 \rangle$ is calculated using the formula $\sqrt{x^2 + y^2}$, which gives $\sqrt{11^2 + 7^2} = \sqrt{121 + 49} = \sqrt{170}$. The direction angle $\theta$ can be found using the formula $\tan^{-1}\left(\frac{y}{x}\right)$, which gives $\tan^{-1}\left(\frac{7}{11}\right)$. This results in an angle of approximately 32.5°, which is in the first quadrant, indicating the vector points in a direction between 0° and 90°.

Find the Magnitude and Direction Angle for the Following Vector ⟨11,7⟩\langle 11,7 \rangle⟨11,7⟩

Find the Magnitude and Direction Angle for the Following Vector $\langle 11,7 \rangle$