Home
Class 12
MATHS
vec a .[(vec b + vec c) xx (vec a + vec ...

`vec a .[(vec b + vec c) xx (vec a + vec b + vec c)] = `

A

0

B

`[vec a vec b vec c].[vec b vec c vec a]`

C

`[vec a vec b vec c]`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|194 Videos

Similar Questions

Explore conceptually related problems

(vec b xx vec c) xx (vec c xx vec a ) =

The vectors vec a + vec b + vec c, 2 vec a+ vec b + 3 vec c and vec a + 2 vec b + 3 vec c , where vec a, vec b , and vec c are non coplanar vectors , are

If (vec a xx vec b) xx vec c = vec a xx (vec b xx vec c) , where vec a, vec b and vec c are any three vectors such that vec a. vec b ne 0, vec b . vec c ne 0 , then vec a and vec c are

For any three vectors vec a, vec b, vec c the expression (vec a - vec b) . [(vec b - vec c ) xx (vec c - vec a)] =

If vec a, vec b, vec c are three vectors such that vec a . (vec b + vec c) + vec b . (vec c + vec a) + vec c . (vec a + vec b) = 0 and |vec a| = 1, |vec b | = 4, |vec c| = 8 , then |vec a + vec b + vec c| =

The three points whose position vectors are vec a - vec 2b + 3 vec c, vec 2a + vec 3b - 4 vec c and - 7 vec b + 10 vec c

If vec a, vec b and vec c are non coplanar then vec a . { (vec b xx vec c)/(3vec b . (vec c xx vec a))}- vec b . {(vec c xx veca)/(2vecc. (veca xx vec b))} =

If vec a, vec b , and vec c are vectors such that |vec b| = |vec c| , then {[(vec a + vec b) xx (vec a + vec c)] xx (vec b xx vec c)} . (vec b + vec c) =

If vec a, vec b, vec c are non coplanar vectors such that, vec b xx vec c = vec a, vec c xx vec a = vec b, vec a xx vec b = vec c , then |vec a + vec b + vec c| =

HIMALAYA PUBLICATION-VECTORS AND THEIR APPLICATIONS-QUESTION BANK
  1. If vec a + vec b + vec c = 0 and |vec a|= 3, |vec b| = 4 and |vec c| =...

    Text Solution

    |

  2. Two planes are perpendicular to one another. One of then contains vect...

    Text Solution

    |

  3. vec a .[(vec b + vec c) xx (vec a + vec b + vec c)] =

    Text Solution

    |

  4. A unit vector perpendicular to both i+j and j+k is

    Text Solution

    |

  5. If vec a, vec b, vec c are non-coplanar vectors and lambda is a real n...

    Text Solution

    |

  6. If the volume of the parallelopiped with veca,vecb and vecc as cotermi...

    Text Solution

    |

  7. The volume of the tetracedron formed by the points (1,1,1) (2,1,3),(3,...

    Text Solution

    |

  8. If vec u = vec a - vec b, vec nu = vec a + vec b and |vec a| = |vec b|...

    Text Solution

    |

  9. Unit vector perpendicular to hati - 2 hatj + 2hatk and lying in the pl...

    Text Solution

    |

  10. If vec u , vec nu, and vec w are non coplanar vectors and p,q are real...

    Text Solution

    |

  11. If vec a . i = vec a . (i+j) = vec a . (i+j+k) = 1, then vec a =

    Text Solution

    |

  12. If vec a and vec b are unit vectors such that |vec a + vec b| =1, then...

    Text Solution

    |

  13. The projection of a = 3i - j + 5k on b = 2i + 3j +k is

    Text Solution

    |

  14. If vec a. vec b = ~ |vec a||vec b| then angle between vec a and vec b ...

    Text Solution

    |

  15. If vec a + 2 vec b + 3 vec c = vec 0, then (vec a xx vec b)+ (vec b xx...

    Text Solution

    |

  16. If vec a, vec b, vec c non zero coplanar vectors, then, [2 vec a - vec...

    Text Solution

    |

  17. If vec(a),vec(b) and vec(c) are unit vectors such that vec(a)+vec(b)+v...

    Text Solution

    |

  18. If the points with position vectors 10 hati + 3 hatj, 12 hati- 5 hatj ...

    Text Solution

    |

  19. If 2hati+3hatj,hati+hatj+hatk and lambdahati+4hatj+2hatk taken in an o...

    Text Solution

    |

  20. If vec a, vec b and vec c are non coplanar then vec a . { (vec b xx ve...

    Text Solution

    |