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If two out to the three vectors , veca, ...

If two out to the three vectors , `veca, vecb , vecc` are unit vectors such that ` veca + vecb + vecc =0 and 2(veca.vecb + vecb .vecc + vecc.veca) +3=0` then the length of the third vector is

A

3

B

2

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
Let ` |veca|-1 and |vecb| =1`
we have,
` veca + vecb+ vecc = vec0`
` Rightarrow |veca|^(2) + |vecb|^(2) + 2 (veca.vecb +vecb.vecc + vecc.veca)=0`
` Rightarrow 1+1 + |vecc|^(2) -3=0 Rightarrow |vecc| =1`
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