Home
Class 12
MATHS
If veca, vecb and vecc are three non-cop...

If `veca, vecb and vecc` are three non-coplanar vectors, then `(veca + vecb + vecc). [(veca + vecb) xx (veca + vecc)]` equals

A

0

B

`[veca vecb vecc]`

C

`2[veca vecb vecc]`

D

`-[veca vecb vecc]`

Text Solution

Verified by Experts

The correct Answer is:
d
`(veca+ vecb+vecc).[(veca+vecb)xx(veca+vecc)]`
`= (veca+vecb+vecc).[veca xx veca +vecaxx vecc+vecb xx veca +vecbxxvecc]`
`= (veca +vecb +vecc).[veca xx vecc +vecb xx veca+vecb xxvecc]`
`[veca vecb vecc] -[veca vecb vecc]-[veca vecb vecc]`
`-[veca vecb vecc]`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise True and false|3 Videos

  • DETERMINANTS

    CENGAGE ENGLISH|Exercise All Questions|264 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos
CENGAGE ENGLISH-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -single correct answer type
  1. If veca,vecb and vecc are non coplanar and unit vectors such that veca...

    Text Solution

    |

  2. Let vecu,vecv and vecw be vectors such that vecu+ vecv + vecw =0 if |v...

    Text Solution

    |

  3. If veca, vecb and vecc are three non-coplanar vectors, then (veca + ve...

    Text Solution

    |

  4. vecp, vecq and vecr are three mutually prependicular vectors of the sa...

    Text Solution

    |

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

    Text Solution

    |

  6. Let veca = 2i + j+k, vecb = i+ 2j -k and a unit vector vecc be coplana...

    Text Solution

    |

  7. If the vectors veca, vecb and vecc form the sides, BC , CA and AB, res...

    Text Solution

    |

  8. Let vectors veca, vecb veca and vecd be such that (veca xxvecb)xx (vec...

    Text Solution

    |

  9. If veca,vecb, vecc are unit coplanar vectors then the scalar triple pr...

    Text Solution

    |

  10. if hata, hatb and hatc are unit vectors. Then |hata - hatb|^(2) + |hat...

    Text Solution

    |

  11. If veca and vecb are two unit vectors such that veca + 2vecb and 5 vec...

    Text Solution

    |

  12. Let vecV = 2hati +hatj - hatk and vecW= hati + 3hatk . if vecU is a u...

    Text Solution

    |

  13. Find the value of a so that the volume of the parallelopiped formed b...

    Text Solution

    |

  14. If veca = (hati + hatj +hatk), veca. vecb= 1 and vecaxxvecb = hatj -ha...

    Text Solution

    |

  15. The unit vector which is orthogonal to the vector 5hati + 2hatj + 6hat...

    Text Solution

    |

  16. If veca , vecb and vecc are three non-zero, non- coplanar vectors and ...

    Text Solution

    |

  17. Let veca=hati + 2hatj +hatk, vecb=hati - hatj +hatk andvecc= hathatj-h...

    Text Solution

    |

  18. Let two non-collinear unit vectors veca and vecb form an acute angle. ...

    Text Solution

    |

  19. If veca, vecc, vecc and vecd are unit vectors such that (vecaxx vecb)....

    Text Solution

    |

  20. Two adjacent sides of a parallelogram A B C D are given by vec A B...

    Text Solution

    |