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Let overset(to)(u),overset(to)(v) " and ...

Let `overset(to)(u),overset(to)(v) " and " overset(to)(W)` be vectors such that `overset(to)(u)+overset(to)(v)+overset(to)(W)=overset(to)(0).` If `|overset(to)(u)|=3.|overset(to)(V)|=4" and " |overset(to)(W)|=5 " then " overset(to)(u).overset(to)(v)+overset(to)(v).overset(to)(w)+overset(to)(w).overset(to)(u)` is

A

47

B

-25

C

0

D

25

Text Solution

Verified by Experts

The correct Answer is:
B
Since `vec(u) +vec(v)+vec(w) =vec(0) rArr |vec(u)+vec(v)+vec(w)|^(2)=0`
`rArr |vec(u)|^(2)+|vec(v)|^(2)+|vec(w)|^(2)(vec(u)". "vec(v)+vec(v)". "vec(w) +vec(w) ". " vec(u))=0`
`rArr 9+ 16 + 25 +2 (vec(u)". " vec(v) + vec(w) ". " vec(w) +vec(w) ". " vec(u)) =0`
`rArr vec(u) ". " vec(v)+ vec(v)". " vec(w) + vec(w) + vec(w) ". " vec(u)=-25`
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