If x and y are two unit vectors and theta is | vedclass

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(B) Given that $x$ and $y$ are unit vectors,so $|x| = 1$ and $|y| = 1$.Let $	heta$ be the angle between $x$ and $y$.We know that $|x - y|^2 = (x - y)

Vedclass · Accepted Answer

$\sin(	heta/2)$

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

If $x$ and $y$ are two unit vectors and $\theta$ is the angle between them,then $\frac{1}{2}|x-y|$ is equal to

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