If angle between two unit vectors `veca` and `vecb` is `theta` then `sin(theta/2)` is equal to

Options

A. `|a-b|//2`
B. `|a+b|//2`
C. `|a-b|`
D. `|a+b|`

Answer

A

Explanation

Now,
`|a-b|=sqrt(a^(2)+b^(2)-2|a||b|costheta)`
`=sqrt(2a^(2)(1-costheta)`
`[because|a|=|b|=a]`
`=sqrt(4a^(2)"sin"^(2)(theta)/(2))=2a"sin"(theta)/(2)`
`impliesa" sin"(theta)/(2)=(|a-b|)/(2)`