Let |u| = 4 at an angle of 210° and |v| = 9 at an angle of 315°, and w = u – v. What is the magnitude and direction angle of w?

Convert each vector to components: u = (4 cos 210°, 4 sin 210°) ≈ (−3.46, −2.00), and v = (9 cos 315°, 9 sin 315°) ≈ (6.36, −6.36). Then w = u − v ≈ (−9.83, 4.36), so its magnitude is √[(−9.83)² + 4.36²] ≈ 10.8. Since w is in Quadrant II, its direction angle is about 156.1°, making the correct choice the vector with magnitude 10.8 and angle 156.1°.

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