If A = cos(ωt)î + sin(ωt)ĵ and B = cos(ωt/2)î + sin(ωt/2)ĵ, find the first positive time at which A and B are perpendicular.
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Question

If A = cos(ωt)î + sin(ωt)ĵ and B = cos(ωt/2)î + sin(ωt/2)ĵ, find the first positive time at which A and B are perpendicular.

G1 Physics · Accepted Answer

Step 1 — Principle: Two vectors are perpendicular when their scalar product equals zero. Step 2 — Working: A·B = cos(ωt)cos(ωt/2)+sin(ωt)sin(ωt/2)=cos(ωt/2). Step 3 — Working: Orthogonality requires cos(ωt/2)=0, so the first positive t=π/ω. Correct answer: A — π/ω.