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Let the vectors veca , vecb , vec c repr...

Let the vectors `veca , vecb , vec c` represent three coterminous edges of a parallelopiped of volume V. Then the volume of the parallelopiped, whose coterminous edges are represented by `veca, vecb+vecc` and `veca+2vecb+3vecc` is equal to

A

`6V`

B

`V`

C

`3V`

D

`2V`

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Statement 1: Let veca, vecb, vecc be three coterminous edges of a parallelopiped of volume V . Let V_(1) be the volume of the parallelopiped whose three coterminous edges are the diagonals of three adjacent faces of the given parallelopiped. Then V_(1)=2V . Statement 2: For any three vectors, vecp, vecq, vecr [(vecp+vecq, vecq+vecr,vecr+vecp)]=2[(vecp,vecq,vecr)]

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Let veca, vecb, vecc be three unit vectors such that veca. vecb=veca.vecc=0 , If the angle between vecb and vecc is (pi)/3 then the volume of the parallelopiped whose three coterminous edges are veca, vecb, vecc is

If the volume of the parallelopiped formed by the vectors veca, vecb, vecc as three coterminous edges is 27 units, then the volume of the parallelopiped having vec(alpha)=veca+2vecb-vecc, vec(beta)=veca-vecb and vec(gamma)=veca-vecb-vecc as three coterminous edges, is

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)

If V is the volume of the 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

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