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The resultant of two vectors ⃗A and ⃗B is perpendicular to ⃗A and its magnitude is half that of ⃗B. The angle between vectors ⃗A and ⃗B is ______°.

Asked in JEE Main 9th April 2nd Shift 2024 · Magnitude of the resultant

Answer: 150

Step-by-step solution

Resultant ⊥ ⃗A: the component of ⃗B along ⃗A cancels ⃗A, so A + B cos θ = 0, i.e. cos θ = -/AB.

Magnitude: R² = A² + B² + 2AB cos θ = B² - A² = (B²)/4 ⇒ A = (√3)/2B.

cos θ = -(√3)/2 ⇒ θ = 150°.

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