If two vectors A and B having equal magnitude R are inclined at angle θ, then (a) |A + B| = 2Rcos ((θ)/(2)) (b) |A - B| = 2Rcos ((θ)/(2)) (c) |A - B| = √(2)Rsin ((θ)/(2)) (d) |A + B| = 2Rsin ((θ)/(2))

Answer: (a). |A + B|² = 2R²(1 + cos θ) = 4R²cos ²(θ)/(2) |A + B| = 2Rcos (θ)/(2) (and |A - B| = 2Rsin (θ)/(2), so (b), (c), (d) are wrong) So the answer is (a).

If two vectors A and B having equal magnitude R are inclined at angle… | JEE Main 2024 (31 Jan, Shift 2)

Q10JEE Main 2024 · 31 JAN · SHIFT 2Easy

Addition & Subtraction of Vectors

If two vectors $\vec{A}$ and $\vec{B}$ having equal magnitude $R$ are inclined at angle $\theta$ , then

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Answer: (a)

$|\vec{A} + \vec{B}|^2 = 2R^2(1 + \cos\theta) = 4R^2\cos^2\frac{\theta}{2}$
$|\vec{A} + \vec{B}| = 2R\cos\frac{\theta}{2}$ (and $|\vec{A} - \vec{B}| = 2R\sin\frac{\theta}{2}$ , so (b), (c), (d) are wrong)
So the answer is (a).

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