Given three vectors `veca,vecbandvecc` each two of which are non-collinear. Further if `(veca+vecb)` is collinear with `vecc,(vecb+vecc)` is collinear with `vecaand|veca|=|vecb|=|vecc|=sqrt(2)`. Then the value of `veca.vecb=vecb.vecc+vecc.veca=`

Options

A. 3
B. -3
C. 0
D. cannot be evaluated

Answer

B

Explanation

`veca+vecb=lamdavecc`
and `vecb+vecc=muveca`
`therefore(lamdavecc-veca)+vecc=muveca("putting "vecb=lamdavecc-veca)`
`rArr(lamda+1)vecc=(mu+1)veca`
`rArrlamda=mu=-1` ltBrgt `rArrveca+vecb+vecc=0` ltBrgt `rArr|veca|^(2)+|vecb|^(2)+|vecc|^(2)+2(veca.vecb+vecb.vecc+vecc.veca)=0`
`rArrveca.vecb+vecb.vecc+vecc.veca=-3`