Home
Class 12
MATHS
If [ veca vecbvecc]=2 , then find the va...

If `[ veca vecbvecc]=2` , then find the value of `[(veca+2vecb-vecc) (veca - vecb) (veca - vecb-vecc)]`

Text Solution

Verified by Experts

`[(veca+2vecb-vecc)(veca-vecb)(veca-vecb-vecc)]`
`=|{:(1,2,-1),(1,-1,0),(1,-1,-1):}|[veca vecbvecc]`
`= 2[veca vecb vecc] = 6`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

  • DETERMINANTS

    CENGAGE|Exercise Question Bank|23 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|25 Videos

Similar Questions

Explore conceptually related problems

If veca, vecb and vecc are three non - zero and non - coplanar vectors such that [(veca,vecb,vecc)]=4 , then the value of (veca+3vecb-vecc).((veca-vecb)xx(veca-2vecb-3vecc)) equal to

If |veca|=3, |vecb|=1, |vecc|=4 and veca + vecb + vecc= vec0 , find the value of veca.vecb+ vecb+ vecc.vecc + vecc.veca .

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

If veca, vecb and vecc be any three non coplanar vectors. Then the system of vectors veca\',vecb\' and vecc\' which satisfies veca.veca\'=vecb.vecb\'=vecc.vecc\'=1 veca.vecb\'=veca.veca\'=vecb.veca\'=vecb.vecc\'=vecc.veca\'=vecc.vecb\'=0 is called the reciprocal system to the vectors veca,vecb, and vecc . The value of [veca\' vecb\' vecc\']^-1 is (A) 2[veca vecb vecc] (B) [veca,vecb,vecc] (C) 3[veca vecb vecc] (D) 0

If veca=hati+hatj+hatk,hatb=hati-hatj+hatk,vecc=hati+2hatj-hatk , then find the value of |{:(veca.veca,veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc):}|

If veca=hati+hatj+hatk,hatb=hati-hatj+hatk,vecc=hati+2hatj-hatk , then find the value of |{:(veca.veca,veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc):}|

If veca, vecb, vecc are any three non coplanar vectors, then [(veca+vecb+vecc, veca-vecc, veca-vecb)] is equal to

For any three vectors veca, vecb, vecc the value of [(veca-vecb, vecb-vecc, vecc-veca)] , is

For three vectors veca, vecb and vecc , If |veca|=2, |vecb|=1, vecaxxvecb=vecc and vecbxxvecc=veca , then the value of [(veca+vecb,vecb+vecc,vecc+veca)] is equal to

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If [ veca vecbvecc]=2 , then find the value of [(veca+2vecb-vecc) (vec...

    Text Solution

    |

  2. Find |veca| and |vecb| if (veca+vecb).(veca-vecb)=8 and |veca|=8|vecb|...

    Text Solution

    |

  3. Show that |veca|vecb+|vecb|veca is perpendicular to |veca|vecb-|vecb|v...

    Text Solution

    |

  4. If the vectors A ,B ,C of a triangle A B C are (1,2,3),(-1,0,0),(0,1,2...

    Text Solution

    |

  5. If |veca|=3, |vecb|=4 and the angle between veca and vecb is 120^(@) ....

    Text Solution

    |

  6. If vectors hati-2xhatj-3yhatk and hati+ 3 x hatj + 2yhatk are orthogon...

    Text Solution

    |

  7. Let veca vecb and vecc be pairwise mutually perpendicular vectors, suc...

    Text Solution

    |

  8. If veca +vecb +vecc=0, |veca|=3,|vecb|=5, |vecc|=7 , then find the ang...

    Text Solution

    |

  9. If the angle between unit vectors veca and vecb is 60^(@) . Then find ...

    Text Solution

    |

  10. Let vecu=hai+hatj,vecv=hati-hatj and vecw=hati+2hatj+3hatk. If hatn is...

    Text Solution

    |

  11. A , B , C , D are any four points, prove that vec A Bdot vec C D+ ...

    Text Solution

    |

  12. P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(,-2,-1), then find the projection...

    Text Solution

    |

  13. If the vectors 3vecP+vecq, 5vecP - 3vecq and 2 vecp+ vecq, 4 vecp - 2v...

    Text Solution

    |

  14. Let vecA and vecB be two non-parallel unit vectors in a plane. If (alp...

    Text Solution

    |

  15. Let veca , vecb and vecc be unit vectors such that veca+vecb+vecc=vecx...

    Text Solution

    |

  16. If veca and vecb are unit vectors, then find the greatest value of |ve...

    Text Solution

    |

  17. Constant forces P(1)=hati-hatj+hatk, P(2)= -hati+2hatj-hatik and P(3)=...

    Text Solution

    |

  18. Find |veca| and |vecb| if (veca+vecb).(veca-vecb)=8 and |veca|=8|vecb|...

    Text Solution

    |

  19. If A ,B ,C ,D are four distinct point in space such that A B is not...

    Text Solution

    |

  20. If veca=2hati+ 3hatj-5hatk,vecb =m hati+nhatj +12 hatk and veca xx vec...

    Text Solution

    |

  21. Find veca.vecb if |veca|2, |vecb|=5,a and |vecaxxvecb|=8

    Text Solution

    |