If theta is the angle between two unit vector | vedclass

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(A) Given that $a$ and $b$ are unit vectors,so $|a| = 1$ and $|b| = 1$. We know that $|a - b|^2 = |a|^2 + |b|^2 - 2(a \cdot b)$. Since $a \cdot b = |a

Vedclass · Accepted Answer

$\frac{1}{2}|a - b|$

Vedclass · Answer

(A) Given that $a$ and $b$ are unit vectors,so $|a| = 1$ and $|b| = 1$. We know that $|a - b|^2 = |a|^2 + |b|^2 - 2(a \cdot b)$. Since $a \cdot b = |a||b| \cos 	heta = (1)(1) \cos 	heta = \cos 	heta$,we have: $|a - b|^2 = 1^2 + 1^2 - 2 \cos 	heta = 2 - 2 \cos 	heta = 2(1 - \cos 	heta)$. Using the trigonometric identity $1 - \cos 	heta = 2 \sin^2(	heta/2)$,we get: $|a - b|^2 = 2(2 \sin^2(	heta/2)) = 4 \sin^2(	heta/2)$. Taking the square root on both sides,we get $|a - b| = 2 \sin(	heta/2)$. Therefore,$\sin(	heta/2) = \frac{1}{2}|a - b|$.

If $\theta$ is the angle between two unit vectors $a$ and $b$,then $\sin(\theta/2) = $ ......

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