Let u = ⟨–2, 6⟩, v = ⟨3, 2⟩, and w = ⟨–1, 4⟩. What is the magnitude and direction angle of 2(u + v) – 3w?

First, u + v = ⟨1, 8⟩, so 2(u + v) = ⟨2, 16⟩. Also, 3w = ⟨−3, 12⟩, giving 2(u + v) − 3w = ⟨5, 4⟩. Its magnitude is √(5² + 4²) = √41 ≈ 6.4, and its direction angle is arctan(4/5) ≈ 38.7°. The correct choice is B: 6.4; θ = 38.7°.

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