Vectors A and B have magnitudes 5 and 10. Their resultant A+B is perpendicular to A. Find the angle between them.
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Question

Vectors A and B have magnitudes 5 and 10. Their resultant A+B is perpendicular to A. Find the angle between them.

G1 Physics · Accepted Answer

A·(A+B)=0 ⇒ A²+A·B=0 ⇒ A·B=−25. Thus cosθ=−25/(50)=−1/2, so θ=120°.