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°].
-$\langle \sqrt { 14 } , - 1 \rangle$
A) $\sqrt { 15 } ; 285 ^ { \circ }$
B) $\sqrt { 15 } ; 345 ^ { \circ }$
C) $15 ; 345 ^ { \circ }$
D) $15 ; 105 ^ { \circ }$

Question

Quizplus · Accepted Answer

The magnitude is $\sqrt{(\sqrt{14})^2 + (-1)^2} = \sqrt{15}$. The direction angle is $\tan^{-1}(-1/\sqrt{14})$, which is in the fourth quadrant, giving approximately 345°.

Find the Magnitude and Direction Angle (To the Nearest Tenth) ⟨14,−1⟩\langle \sqrt { 14 } , - 1 \rangle⟨14​,−1⟩

Find the Magnitude and Direction Angle (To the Nearest Tenth) $\langle \sqrt { 14 } , - 1 \rangle$