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Two vectors A and B combine to give a resultant that is perpendicular to A, and the magnitude of this resultant is one-half the magnitude of B. What is the angle between A and B?

1. 120°
2. 150°
3. 135°
4. 180°

Correct answer: 150°

Solution

R=A+B perp to A: A^2 + A.B = 0. |R|^2 = A^2+2A.B+B^2 = B^2-A^2 = B^2/4 -> A^2 = 3B^2/4. cos(theta)=A.B/(AB) = -A^2/(AB) = -A/B = -sqrt3/2, so theta = 150 deg.

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