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 _________ °. Numerical answer type. Work it out, then open the answer.

Answer: 150. Resultant ⊥ A: A + Bcos θ = 0, so cos θ < 0 (obtuse angle). Then R = Bsin θ; given R = B/2 ⇒ sin θ = 1/2. Obtuse angle with sin θ = 1/2 is θ = 150°. Answer: 150°

The resultant of two vectors A and B is perpendicular to A and its… | JEE Main 2024 (9 Apr, Shift 2)

Q11JEE Main 2024 · 9 APR · SHIFT 2Medium

Addition & Subtraction of Vectors

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$ . The angle between vectors $\vec{A}$ and $\vec{B}$ is _________ ${}^\circ$ .

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 150

Resultant $\perp \vec{A}$ : $A + B\cos\theta = 0$ , so $\cos\theta < 0$ (obtuse angle).
Then $R = B\sin\theta$ ; given $R = \frac{B}{2} \Rightarrow \sin\theta = \frac{1}{2}$ .
Obtuse angle with $\sin\theta = \frac{1}{2}$ is $\theta = 150^\circ$ .
Answer: $150^\circ$

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