Let vector a with components five comma negative nine and vector b with components negative 3 comma 1 , and vector c is equal to vector b minus vector a What is the magnitude and direction angle of vector c ?

Subtract the components to find vector c: c = b − a = (−3 − 5, 1 − (−9)) = (−8, 10). Its magnitude is √((−8)² + 10²) = √164 ≈ 12.8. Since c is in Quadrant II, its direction angle measured counterclockwise from the positive x-axis is about 128.7°. Therefore, the correct choice is D: magnitude 12.8 and angle 128.7°.

AI-written and checked against the verified answer.