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If `Veca","Vecb","Vecc`Are Unit Vectors Such That `Veca+Vecb+Vecc=0`, Then Write the Value Of `Veca.Vecb+Vecb.Vecc+Vecc.Veca` - CBSE (Science) Class 12 - Mathematics

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Question

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

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?
Solution If `Veca","Vecb","Vecc`Are Unit Vectors Such That `Veca+Vecb+Vecc=0`, Then Write the Value Of `Veca.Vecb+Vecb.Vecc+Vecc.Veca` Concept: Product of Two Vectors - Scalar (Or Dot) Product of Two Vectors.
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