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Let veca, vecb and vecc are three unit v...

Let `veca, vecb` and `vecc` are three unit vectors in a plane such that they are equally inclined to each other, then the value of `(veca xx vecb).(vecb xx vecc) + (vecb xx vecc). (vecc xx veca)+(vecc xx veca). (veca xx vecb)` can be

A

`9/4`

B

`-9/4`

C

`3/4`

D

`-3/4`

Text Solution

Verified by Experts

The correct Answer is:
A
Since `veca, vecb` and `vecc` are in a plane and equally inclined to each other, then angle between any two vectors is `120^(@)` and `(veca xx vecb), (vecb xx vecc)` and `(vecc xx veca)` are parallel.
So, `(veca xx vecb).(vecb xx vecc) = |veca xx vecb||vecb xx vecc|.costheta`
`=sqrt(3)/2.sqrt(3)/2.1=3/4`
Similarly, `(vecb xx vecc). (vecc xx veca) = 3/4` and `(vecc xx veca).(veca xx vecb) =3/4`
`rArr "sum"=3/4+3/4+3/4=9/4`
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