Home
Class 12
MATHS
If ABCD is a quadrilateral with vec AB =...

If ABCD is a quadrilateral with `vec AB = vec a, vec AD = vec b` and `vec AC = 2 vec a + 3 vec b`. If its areas is `alpha` times the area of the parallelogram with AB, AD as adjacent sides than `alpha =`

A

5

B

`5/2`

C

1

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|194 Videos

Similar Questions

Explore conceptually related problems

If OACB is a parallelogram with vec OC = vec a and vec AB = vec b then vec OA =

If vec a xx vec b = vec c and vec b xx vec c = vec a then

[vec a + vec b vec b + vec c vec c + vec a] =

If vec a = i+j+k, vec a. vec b = 1 and vec a xx vec b = j-k then vec b =

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

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

If |vec a| =5, |vec b| =6, vec a . vec b = 24 then |vec a xx vec b| =

If |vec a| = 2, |vec b| = 5 and |vec a xx vec b| = 8 then vec a . vec b

HIMALAYA PUBLICATION-VECTORS AND THEIR APPLICATIONS-QUESTION BANK
  1. Let vec a, vec b and vec c of magnitudes 3,4 and 5 repectively. If vec...

    Text Solution

    |

  2. If ai+j+k, i+bj+k and i+j+ck are coplanar, then

    Text Solution

    |

  3. If ABCD is a quadrilateral with vec AB = vec a, vec AD = vec b and vec...

    Text Solution

    |

  4. A unit vector coplanar with i+j+2k and i+2j+k and perpendicular to i+j...

    Text Solution

    |

  5. If vec a, vec b and vec c are non coplanar unit vectors such that vec ...

    Text Solution

    |

  6. Let vec a = i-j, vec b = j-k, vec c = k-i. If vec d is a unit vectors ...

    Text Solution

    |

  7. Let vec a, vec b and vec c be three vectors having magnitudes 1,1, and...

    Text Solution

    |

  8. If vec a, vec b, and vec c are vectors such that |vec b| = |vec c|, th...

    Text Solution

    |

  9. Let vec a and vec b be two non collinear unit vectors. If vec u = vec ...

    Text Solution

    |

  10. If vec a = 2i+j+k, vec b = i + 2j-k and a unit vector vec c be coplana...

    Text Solution

    |

  11. Let vec a = 2i+j-2k and vec b = i+j. If vec c is a vector such that ...

    Text Solution

    |

  12. Let vec a, vec b and vec c are unit coplanar vectors then the scalar t...

    Text Solution

    |

  13. If vec a, vec b, vec c are unit vectors then |vec a - vec b|^(2) + |ve...

    Text Solution

    |

  14. Let vec nu = 2i+j-k and vec w = i+3k. If vec u is a unit vector, then ...

    Text Solution

    |

  15. If vec a and vec b are two unit vectors such that vec a + 2 vec b and ...

    Text Solution

    |

  16. The valur of a so that the volume of parallelopiped formed by vectors ...

    Text Solution

    |

  17. If vec a = i+j+k, vec a. vec b = 1 and vec a xx vec b = j-k then vec b...

    Text Solution

    |

  18. The unit vector which is orthogonal to the vector vec a = 3i+2j+6k and...

    Text Solution

    |

  19. If vec a and vec b are two unit vectors, then the vector (vec a + vec ...

    Text Solution

    |

  20. Given vec a = i+j-k, vec b = -i+2j+k and vec c = -i+2j-k, a unit vecto...

    Text Solution

    |