Find the magnitude and positive direction angle of the vector <4 radical 3 , – 4 >

Question

I got magnitude = 8 and angle = 330 degrees I just want to make sure I did it right. Thank you

Answer 1

Magnitude: √((4√3)²+ (-4)²) = √(48 + 16) = √64 = 8

Angle: arctan(|-4/(4√3)|) = arctan(1/√3) = 30°

Since we know the vector appears in quadrant IV and has a reference angle of 30°, we know the positive direction angle is 330°.