Let a = ⟨5, –9⟩ and b = ⟨–3, 1⟩, and c = b – a. What is the magnitude and direction angle of c?

Subtract the vectors componentwise: 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 is 180° − arctan(10/8) ≈ 128.7°. Therefore, the correct choice is A: |c| = 12.8; θ = 128.7°.

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