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Let veca, vecb , vecc be three vectors ...

Let ` veca, vecb , vecc` be three vectors of equal magnitude such that the angle between each pair is ` pi/3` . If ` |veca + vecb + vecc| = sqrt6` , then `|veca|=`

A

2

B

-1

C

1

D

`- sqrt(2/3)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let ` |veca|=|vecb|=|vecc|= lambda`, then,
`veca .vecb = vecc= vecc .veca = (lambda^(2))/2`
Now,
`|veca + vecb + vecc|=sqrt6`
` Rightarrow |veca + vecb + vecc| ^(2) =6`
` Rightarrow |veca|^(2) +|vecb|^(2) +|vecc|^(2) + 2( veca. vecb+vecb .vecc + vecc.veca) =6`
` Rightarrow |veca|^(2) +|vecb|^(2) +|vecc|^(2) + 2(veca.vecb + vecb.vecc+ vecc.veca)=6`
` Rightarrow 6lambda^(2) =1 Rightarrow lambda=1 Rightarrow |veca|=1 `
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