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°].
--5, 12
A) 15; 112.6°
B) 13; 157.4°
C) 13; 67.4°
D) 13; 112.6°

Question

Quizplus · Accepted Answer

The magnitude of the vector (-5, 12) is √((-5)^2 + 12^2) = √(25 + 144) = √169 = 13. The direction angle θ is found using tan(θ) = 12/(-5), which gives θ = arctan(-12/5). This angle is in the second quadrant, so θ = 180° - |arctan(12/5)| ≈ 112.6°.

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