Home
Class 12
MATHS
If V is the volume of the parallelopiped...

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

A

`V^(3)`

B

3V

C

`V^(2)`

D

2V

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Similar Questions

Explore conceptually related problems

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 parallelepiped having three coterminous edges as veca,vecb and vecc , then the volume of the parallelepiped having three coterminous edges as vecalpha = (veca.veca)veca+(veca.vecb)vecb+(veca.vecc)vecc , vecbeta=(vecb.veca)veca+(vecb.vecb)+(vecb.vecc)vecc and veclambda=(vecc.veca)veca+(vecc.vecb)vecb+(vecc.vecc)vecc is

The volume of a tetrahedron fomed by the coterminus edges veca , vecb and vecc is 3 . Then the volume of the parallelepiped formed by the coterminus edges veca +vecb, vecb+vecc and vecc + veca 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

Show that [veca vecb vecc]\^2=|(veca.veca,veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc)|

If |{:(veca,vecb,vecc),(veca.veca,veca.vecb,veca.vecc),(veca.vecc,vecb.vecc,veca.vecc)| where veca, vecb,vecc are coplanar then:

If vecA=(vecbxxvecc)/([vecb vecc vecc]), vecB=(veccxxveca)/([vecc veca vecb)], vecC=(vecaxxvecb)/([veca vecb vecc)] find [vecA vecB vecC]

If vector veca,vecb,vecc are coplanar show that |(veca,vecb,vecc),(veca.veca,veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc)|

Prove that [veca+vecb, vecb+vecc ,vecc+veca]=2[veca vecb vecc]