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If V is the volume of the parallelepiped...

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

A

`V^(3)`

B

3V

C

`V^(2)`

D

2V

Text Solution

Verified by Experts

The correct Answer is:
A
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VMC MODULES ENGLISH-VECTORS -LEVEL -1
  1. Let veca, vecb and vecc be non-zero vectors such that no two are colli...

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  2. If veca and vecb are mutually perpendicular unit vectors, vecris a vec...

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  3. If V is the volume of the parallelepiped having three coterminous edge...

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  4. Let G(1), G(2) and G(3) be the centroid of the triangular faces OBC, O...

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  5. If hati, hatj, hatk are unit orthonormal vectors and veca is a vector,...

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  6. The vector vec a has the components 2p and 1 w.r.t. a rectangular C...

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  7. If the vectors veca=hati+ahatj+a^(2)hatk, vecb=hati+bhatj+b^(2)hatk, v...

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  8. If veca =hati + hatj, vecb = hati - hatj + hatk and vecc is a unit vec...

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  9. If the vectors veca and vecb are mutually perpendicular, then veca xx ...

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  10. If veca is perpendicular to vecb and vecr is a non-zero vector such th...

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  11. Let veca=hati-hatj, vecb=hatj-hatk, vecc=hatk-hati. If hatd is a unit ...

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  12. Given that veca,vecc,vecd are coplanar the value of (veca + vecd).{vec...

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  13. let veca , vecb and vecc be three vectors having magnitudes 1, 1 and 2...

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  14. If A(1,-1,-3),B(2,1,-2) and C(-5,2,-6) are the position vectors of the...

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  15. If |{:(veca,vecb,vecc),(veca.veca,veca.vecb,veca.vecc),(veca.vecc,vecb...

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  16. Let vec(A)D be the angle bisector of angle A" of " Delta ABC such th...

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  17. Let veca = 2hati + hatj + hatk, and vecb = hati+ hatj if c is a vecto...

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  18. If veca and vecb are two unit vectors and theta is the angle between t...

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  19. If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc...

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  20. If veca,vecb,vecc and vecp,vecq,vecr are reciprocal system of vectors,...

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