If `veca,vecbandvecc` are unit vectors such that `veca+vecb+vecc=0`, then the value of `veca.vecb+vecb.vecc+vecc.veca` is

Options

A. 1
B. 3
C. `-(3)/(2)`
D. None of these

Explanation

We have, `veca+vecb+vecc=0andveca^(2)=1,vecb^(2)=1,vecc=1`
`:'(veca+vecb+vecc)(veca+vecb+vecc)=0`
`impliesveca^(2)+veca.vecb+veca.vecc+vecb.veca+vecb^(2)+vecb.vecc+vecc.veca++vecc^(2)=0`
`impliesveca^(2)+vecb^(2)+vecc^(2)+2(veca.vecb+vecb.vecc+vecc.veca)=0`
`[:'veca.vecb=vecb.veca,vecb.vecc=vecc.vecbandvecc.veca=veca.vecc]`
`implies1+1+1+2(veca.vecb+vecb.vecc+vecc.veca)=0`
`impliesveca.vecb+vec b.vecc+vecc.veca=-(3)/(2)`