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If |vecAxxvecB|=sqrt3vecAvecB, then the ...

If `|vecAxxvecB|=sqrt3vecAvecB`, then the velue of `|vecA+vecB|` is

A

(A^2+B^2+(AB)/(sqrt3))^((1)/(2))`

B

`A+B`

C

`(A^2B^2+sqrt3AB)^((1)/(2))`

D

`(A^2+B^2+AB)^((1)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
`|vecAxxvecB|=sqrt(3)(vecA.vecB)`
AB `sintheta=sqrt(3)Abcosthetaimpliestantheta=sqrt(3)becausetheta=60^@`
Now `|vecR|=|vecA+vecB|=sqrt(A^(2)+B^(2)+2ABcostheta)`
`=sqrt(A^(2)+B^(2)+2AB((1)/(2)))=(A^(2)+B^(2)AB)^((1)/(2))`
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