Help with finding magnitude and direction angle?

Question

Find the magnitude and direction angle of v=-7i+3j

Answer 1

Make a little sketch showing the vector in 'standard position'; its magnitude is √58 (applying Pythagorean theorem).

 

angle θ can be determined as arctan (3/(-7)0 but you will have to make the usual adjustment that is needed since arctan results are in quadrant IV for negative arguments, and quadrant I for positive arguments; i.e. be sure your final angle θ is in quadrant II.