A vector A is rotated by a small angle Δθ radian ( Δθ < <1) to get a new vector B. In that case is: (a) 0 (b) (c) (d)

Answer: (c). |B| = |A| (rotation does not change length); the angle between them is Δθ. |B - A| = 2|A|sin (Δθ)/(2) For Δθ 1, sin (Δθ)/(2) ≈ (Δθ)/(2), so |B - A| ≈ |A|Δθ. So the answer is (c) |A|Δθ.

A vector A is rotated by a small angle Δθ radian ( Δθ < <1) to get a… | JEE Main 2015 (11 Apr, Shift 1)

Q31JEE Main 2015 · 11 APR · SHIFT 1Medium

Addition & Subtraction of Vectors

A vector $\vec{A}$ is rotated by a small angle $\Delta\theta$ radian ( $\Delta\theta$ < <1) to get a new vector $\vec{B}$ . In that case is:

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Answer: (c)

$|\vec{B}| = |\vec{A}|$ (rotation does not change length); the angle between them is $\Delta\theta$ .
$|\vec{B} - \vec{A}| = 2|\vec{A}|\sin\frac{\Delta\theta}{2}$
For $\Delta\theta \ll 1$ , $\sin\frac{\Delta\theta}{2} \approx \frac{\Delta\theta}{2}$ , so $|\vec{B} - \vec{A}| \approx |\vec{A}|\Delta\theta$ .
So the answer is (c) $|\vec{A}|\Delta\theta$ .

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Addition & Subtraction of Vectors question from JEE Main 2015 (11 Apr, Shift 1)

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