यदि एकांक सदिश `hatA` व `hatB` कोण `theta` पर झुके हैं, तो `|hatA-hatB|` हैं -

Options

A. `2sin(theta)/(2)`
B. `2cos(theta)/(2)`
C. `2tan(theta)/(2)`
D. `tantheta`

Answer

A

Explanation

`|vecA-vecB|^(2)=(hatA-hatB).(hatA-hatB)`
`=hatA.hatA-hatA.hatB-hatB.hatA+hatB.hatB`
`=1-hatA.hatB-hatA.hatB+1`
`=2-2costheta=2(1-costheta)`
`=2(2sin^(2).(theta)/(2))=4sin^(2).(theta)/(2)`
`|hatA-hatB|=2sin.(theta)/(2)`