A vector vec{A} is rotated by a small angle D | vedclass

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Question

(A) When a vector $\vec{A}$ is rotated by a small angle $\Delta 	heta$,the magnitude of the vector remains unchanged,so $|\vec{A}| = |\vec{B}| = A$.T

Vedclass · Accepted Answer

$|\vec{A}| \Delta 	heta$

Vedclass · Answer

(A) When a vector $\vec{A}$ is rotated by a small angle $\Delta 	heta$,the magnitude of the vector remains unchanged,so $|\vec{A}| = |\vec{B}| = A$.The difference vector $\vec{B} - \vec{A}$ represents the chord length between the tips of the two vectors.For a very small angle $\Delta 	heta$,the chord length is approximately equal to the arc length of the circle traced by the tip of the vector.Using the relation $	ext{Arc length} = 	ext{radius} 	imes 	ext{angle}$,we have:$|\vec{B} - \vec{A}| \approx |\vec{A}| \Delta 	heta$.

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

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