If `veca","vecb","vecc`are unit vectors such that `veca+vecb+vecc=0`, then write the value of `veca.vecb+vecb.vecc+vecc.veca`
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Solution 1
We have `veca","vecb","vecc`as unit vectors.
Therefore `|veca|=1","|vecb|=1" and"|vecc|=1`
Also `veca+vecb+vecc=0`
`|veca+vecb+vecc|^2=0`
`=>|veca|^2+|vecb|^2+|vecc|^2+2(veca.vecb+vecb.vecc+vecc.veca)=0`
`=>1+1+1+2(veca.vecb+vecb.vecc+vecc.veca)=0`
`=>3+2(veca.vecb+vecb.vecc+vecc.veca)=0`
`=>(veca.vecb+vecb.vecc+vecc.veca)=-3/2`
Solution 2
Is there an error in this question or solution?
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