A vector of magnitude b is rotated through angle `theta`. What is the change in magnitude of the vector?

Options

A. `2b "sin" theta/2`
B. `2b "cos" theta/2`
C. `2b "sin" theta`
D. `2 b cos theta`

Answer

A

Explanation

`vec(PQ)+vec(QR)=vec(PR)`
`therefore vec(QR)=vecb.-vecb`

Now `|vecb.-vecb|^2 =(vecb.-vecb).(vecb.-vecb)`
`=b.^2-2bb. cos theta + b^2 =2b^2 (1-cos theta ) " " [because b.=b]`
`vecb.=vecb=sqrt2bsqrt(1-costheta)=sqrt2 (sqrt2"sin" theta/2)=2b "sin" theta/2`