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If veca,vecb, vecc are three vectors su...

If ` veca,vecb, vecc` are three vectors such that
` veca + vecb +vecc =vec0, |veca| =1 |vecb| =2, | vecc| =3` , then
` veca.vecb + vecb .vecc +vecc + vecc.veca ` is equal to

A

1

B

0

C

-7

D

7

Text Solution

Verified by Experts

The correct Answer is:
C
we have,
` veca + vecb + vecc = vec0`
` Rightarrow |veca + vecb + vecc | = 0`
` Rightarrow |veca + vecb + vecc|^(2) =0`
` Rightarrow |veca|^(2) + |vecb|^(2) + 2 ( veca .vecb + vecb .vecc + vecc. veca) =0`
`Rightarrow 1+4+ 9+2 ( veca .vecb +vecb .vecc + vecc .veca) = 0`
` Rightarrow veca. vecb + vecb.vecc + vecc.veca = - 7 `
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