Let magnitude of u is equal to 10 at an angle of 45 degrees and magnitude of v is equal to 13 at an angle of 150 degrees , and vector w is equal to vector u plus vector v What is the magnitude and direction angle of vector w ?

Resolve each vector into horizontal and vertical components. The sum has components wₓ = 10 cos 45° + 13 cos 150° ≈ −4.19 and wᵧ = 10 sin 45° + 13 sin 150° ≈ 13.57. Thus |w| = √[(−4.19)² + 13.57²] ≈ 14.2. Since the horizontal component is negative and the vertical component is positive, w is in quadrant II, giving a direction angle of about 107.1°. The correct choice is D: magnitude 14.2 and direction angle 107.1°.

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