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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` - Mathematics

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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`

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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

Concept: Product of Two Vectors - Scalar (Or Dot) Product of Two Vectors
  Is there an error in this question or solution?

APPEARS IN

NCERT Class 12 Maths
Chapter 10 Vector Algebra
Q 13 | Page 448
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