If x and y are two unit vectors and the angle | vedclass

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

Vedclass · Accepted Answer

$|\sin(\phi / 2)|$

Vedclass · Answer

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

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

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