Home
Class 12
MATHS
If vecaxx(vecbxxvecc)=(vecaxxvecb)xxvecc...

If `vecaxx(vecbxxvecc)=(vecaxxvecb)xxvecc` for non coplanar `veca,vecb,vecc` then……

A

`(veccxxveca)xx vecb =vec0`

B

`vecc xx (vecaxxvecb)=vec0`

C

`vecbxx (vecc xxveca)=vec0`

D

`veccxxvecaxxvecb=vecb xx (veccxxveca) = vec0`

Text Solution

Verified by Experts

The correct Answer is:
a,c,d
` veca xx (vecbxxvecc)=(vecaxxvecb)xxvecc`
`or (veca.vecc)vecb- (veca. Vecb) vecc = (veca.vecc) vecb- (vecc.vecv)veca `
`or (veca -vecb) vecc - (vecc.vecb)veca=0`
`or (vecc xx veca) xx vecb =0`
`or vecb xx (vecc xx veca) = (vecc xx veca) xx vecb =vec0`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

  • DETERMINANTS

    CENGAGE|Exercise All Questions|268 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

Similar Questions

Explore conceptually related problems

if (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc) where veca,vecb,vecc are any three vectors such that vecb.veccne0 and veca.vecbne0 then veca and vecc are_______

Show that the vectors 2veca-vecb+3vecc, veca+vecb-2vecc and veca+vecb-3vecc are non-coplanar vectors (where veca, vecb, vecc are non-coplanar vectors).

If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd show that veca-vecd and vecb-vecc are parallel.

veca=2hati+hatj+2hatk, vecb=hati-hatj+hatk and non zero vector vecc are such that (veca xx vecb) xx vecc = veca xx (vecb xx vecc) . Then vector vecc may be given as

If vecP = (vecbxxvecc)/([vecavecbvecc]),vecq=(veccxxveca)/([veca vecb vecc])and vecr = (vecaxxvecb)/([veca vecbvecc]), " where " veca,vecb and vecc are three non- coplanar vectors then the value of the expression (veca + vecb + vecc ). (vecp+ vecq+vecr) is

If veca =3veci+2vecj-4veck , vecb =5veci-3vecj+6veck , vecc =5veci+vecj+2veck ,fin(i) vecaxx(vecbxxvecc) (ii) (vecaxxvecb)xxvecc and show that they are not equal.

Prove that (veca.(vecbxxvecc))veca=(vecaxxvecb)xx(vecaxxvecc) .

If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively of a triangle ABC then (A) veca.(vecbxxvecc)=vec0 (B) vecaxx(vecbxvecc)=vec0 (C) veca.vecb=vecc=vecc=veca.a!=0 (D) vecaxxvecb+vecbxxvecc+veccxxvecavec0

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If vectors vecA=2hati+3hatj+4hatk, vecB=hati+hatj+5hatk and vecC form ...

    Text Solution

    |

  2. If veca=xhati + y hatj + zhatk, vecb= yhati + zhatj + xhatk and vecc= ...

    Text Solution

    |

  3. If vecaxx(vecbxxvecc)=(vecaxxvecb)xxvecc for non coplanar veca,vecb,v...

    Text Solution

    |

  4. A vector vecd is equally inclined to three vectors veca=hati-hatj+hatk...

    Text Solution

    |

  5. A parallelogram is constructed on the vectors veca=3vecalpha-vecbeta, ...

    Text Solution

    |

  6. Statement 1: Vector vecc = -5hati + 7 hatj + 2hatk is along the bisec...

    Text Solution

    |

  7. Statement1: A component of vector vecb = 4hati + 2hatj + 3hatk in the ...

    Text Solution

    |

  8. Statement 1: Distance of point D( 1,0,-1) from the plane of points A( ...

    Text Solution

    |

  9. Let vecr be a non - zero vector satisfying vecr.veca = vecr.vecb =vecr...

    Text Solution

    |

  10. Statement 1: If a(1)hati + a(2)hatj + a(3)hatk, b(1)hati+b(2)hatj + b(...

    Text Solution

    |

  11. Statement 1: vecA=2hati + 3hatj + 6hatk , vecB=hati + hatj - 2hatk and...

    Text Solution

    |

  12. Statement 1: veca, vecb and vecc are three mutually perpendicular unit...

    Text Solution

    |

  13. Consider three vectors veca , vecb and vecc Statement 1: vecaxxvecb ...

    Text Solution

    |

  14. Let vecu, vecv and vecw be three unit vectors such that vecu + vecv + ...

    Text Solution

    |

  15. Let vecu, vecv and vecw be three unit vectors such that vecu + vecv + ...

    Text Solution

    |

  16. Let vecu, vecv and vecw be three unit vectors such that vecu + vecv + ...

    Text Solution

    |

  17. Vectors vecx,vecy,vecz each of magnitude sqrt(2) make angles of 60^0 w...

    Text Solution

    |

  18. vertors vecx , vecy and vecz each of magnitude sqrt2 , make an angle ...

    Text Solution

    |

  19. vertors vecx , vecy and vecz each of magnitude sqrt2 , make an angle ...

    Text Solution

    |

  20. If vecx xx vecy=veca, vecy xx vecz=vecb, vecx.vecb=gamma, vecx.vecy=1 ...

    Text Solution

    |