Let |u| = 10 at an angle of 45° and |v| = 13 at an angle of 150°, and w = u + v. What is the magnitude and direction angle of w?

Resolve each vector into components: u ≈ (10 cos 45°, 10 sin 45°) = (7.07, 7.07), and v ≈ (13 cos 150°, 13 sin 150°) = (−11.26, 6.50). Thus w ≈ (−4.19, 13.57), so its magnitude is √((−4.19)² + 13.57²) ≈ 14.2. Since w is in Quadrant II, its direction angle is about 107.1°. The correct choice is D: |w| = 14.2; θ = 107.1°.

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