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If vector A and B have an angle theta be...

If vector A and B have an angle `theta` between them, then value of `|hatA -hatB|` will be

A

`2sin""(theta)/(2)`

B

`2cos""(theta)/(2)`

C

`2tan""(theta)/(2)`

D

`tantheta`

Text Solution

Verified by Experts

The correct Answer is:
A
`|hat(A)-hat(B)|^(2)=|hat(A)|^(2)+|hat(B)|^(2)-2hat(A).hat(B)`
`=2-2costheta=2(1-costheta)" "("":'|hat(A)|=|hat(B)|=1)`
`=2(2sin^(2)""(theta)/(2))=4sin^(2)""(theta)/(2)or|hat(A)-hat(B)|=2sin""(theta)/(2)`
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