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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`

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OBJECTIVE RD SHARMA ENGLISH-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Exercise
  1. Let vec(alpha),vec(beta) and vec(gamma be the unit vectors such that v...

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  2. If veca, vecb and vecc are unit coplanar vectors, then [(2veca-3vecb,...

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  3. If [(veca,vecb,vecc)]=3, then the volume (in cubic units) of the paral...

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

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  5. Unit vectors veca and vecb ar perpendicular , and unit vector vecc is ...

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  6. If vectors vec A B=-3 hat i+4 hat ka n d vec A C=5 hat i-2 hat j+4 ha...

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  7. Let the position vectors of vertices A,B,C of DeltaABC be respectively...

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  8. The position vector of a point P is vecr=xhati+yhatj+zhatk where x,y,z...

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  9. veca and vecb are two unit vectors that are mutually perpendicular. A...

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  10. If the vectors 2ahati+bhatj+chatk, bhati+chatj+2ahatk and chati+2ahatj...

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  11. Let alpha = a hati + b hatj + chatk , vecbeta = bhati + chatj + ahatk ...

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  12. Let veca,vecb,vecc be three mutually perpendicular vectors having same...

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  13. Let veca,vecb and vecc be the three non-coplanar vectors and vecd be a...

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  14. Let vecr be a unit vector satisfying vecr xx veca = vecb, " where " |v...

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  15. Let veca and vecc be unit vectors such that |vecb|=4 and vecaxxvecb=2(...

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  16. If veca+2vecb+3vecc=0, then vecaxxvecb+vecbxxvecc+veccxxveca=

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  17. If in triangle ABC, vec(AB) = vecu/|vecu|-vecv/|vecv| and vec(AC) = (...

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  18. Let A(2hat(i)+3hat(j)+5hat(k)), B(-hat(i)+3hat(j)+2hat(k)) and C(lambd...

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  19. A plane is parallel to the vectors hati+hatj+hatk and 2hatk and anothe...

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  20. If A,B,C,D are four points in space, then |vec(AB)xvec(CD)+vec(BC)xxve...

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