Two vectors A and B have equal magnitudes. If magnitude of A + B is equal to two times the magnitude of A - B, then the angle between A and B will be: (a) sin ⁻¹(3/5) (b) sin ⁻¹(1/3) (c) cos ⁻¹(3/5) (d) cos ⁻¹(1/3)

Answer: (c). Equal magnitudes: |A + B| = 2Acos (θ)/(2), |A - B| = 2Asin (θ)/(2). cos (θ)/(2) = 2sin (θ)/(2) ⇒ tan (θ)/(2) = 1/2 cos θ = (1 - tan ²(θ/2))/(1 + tan ²(θ/2)) = (1 - 1/4)/(1 + 1/4) = 3/5 So the answer is (c) cos ⁻¹(3/5).

Two vectors A and B have equal magnitudes. If magnitude of A + B is… | JEE Main 2022 (29 Jun, Shift 1)

Q15JEE Main 2022 · 29 JUN · SHIFT 1Medium

Addition & Subtraction of Vectors

Two vectors $\vec{A}$ and $\vec{B}$ have equal magnitudes. If magnitude of $\vec{A} + \vec{B}$ is equal to two times the magnitude of $\vec{A} - \vec{B}$ , then the angle between $\vec{A}$ and $\vec{B}$ will be:

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Answer: (c)

Equal magnitudes: $|\vec{A} + \vec{B}| = 2A\cos\frac{\theta}{2}$ , $|\vec{A} - \vec{B}| = 2A\sin\frac{\theta}{2}$ .
$\cos\frac{\theta}{2} = 2\sin\frac{\theta}{2} \Rightarrow \tan\frac{\theta}{2} = \frac{1}{2}$
$\cos\theta = \frac{1 - \tan^2(\theta/2)}{1 + \tan^2(\theta/2)} = \frac{1 - 1/4}{1 + 1/4} = \frac{3}{5}$
So the answer is (c) $\cos^{-1}\left(\frac{3}{5}\right)$ .

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Addition & Subtraction of Vectors question from JEE Main 2022 (29 Jun, Shift 1)

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