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Let vec(a), vec(b), vec(c) are three uni...

Let `vec(a), vec(b), vec(c)` are three unit vector such that `vec(a)+vec(b)+vec(c)` os also a unit vector. If pairwise angles between `vec(a), vec(b), vec(c)` are `theta_(1), theta_(2)` and `theta_(3)` respectively then `cos theta_(1)+cos theta_(2)+ cos theta_(3)` equals

A

`3`

B

`-3`

C

`1`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
D
`:' |hat(a)+hat(b)+hat(c)|=1`
`:. |hat(a)|^(2)+|hat(b)|^(2)+|hat(c)|^(2)+2(hat(a).hat(b)+hat(b).hat(c)+hat(c).hat(a))=1`
`rArr 1+1+1+2(cos theta_(1)+ cos theta_(2)+ cos theta_(3))=1`
`rArr cos theta_(1)+cos theta_(2)+ cos theta_(3)=-1`
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