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Statement 1: If V is the volume of a par...

Statement 1: If `V` is the volume of a parallelopiped having three coterminous edges as `veca, vecb`, and `vecc`, then the volume of the parallelopiped having three coterminous edges as
`vec(alpha)=(veca.veca)veca+(veca.vecb)vecb+(veca.vecc)vecc`
`vec(beta)=(veca.vecb)veca+(vecb.vecb)vecb+(vecb.vecc)vecc`
`vec(gamma)=(veca.vecc)veca+(vecb.vecc)vecb+(vecc.vecc)vecc` is `V^(3)`
Statement 2: For any three vectors `veca, vecb, vecc`
`|(veca.veca, veca.vecb, veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc)|=[(veca,vecb, vecc)]^(3)`

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
We have `|[(veca, vecb, vecc)]|=V`
Let `V_(1)` be the volume of the parallelopiped formed by the vectors `vec(alpha),vec(beta)` and `vec(gamma)`. Then `V_(1)=|[(vec(alpha),vec(beta),vec(gamma))]|`
Now `[(vec(alpha),vec(beta),vec(gamma))]=|(veca.veca, veca.vecb,veca.vecc),(veca.vecb,vecb.vecb,vecb.vecc),(veca.vecc,vecb.vecc.vecc.vecc)|[(veca,vecb,vecc)]`
`implies[(vec(alpha),vec(beta),vec(gamma)]=[(veca,vecb,vecc)]^(2)[(veca,vecb,vecc)]`
`implies[(vec(alpha),vec(beta),(vec(gamma))]=[(veca,vecb,vecc)]^(3)`
`:.V_(1)=|[(vec(alpha),vec(beta),vec(gamma))]|=|[(veca,vecb,vecc)]^(3)|=V^(3)`
Statment -2 is not true.
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