Home
Class 12
MATHS
If vec a, vec b, vec c are non-coplanar ...

If `vec a, vec b, vec c` are non-coplanar vectors and `lambda` is a real number, then `[lambda ( vec a + vec b) lambda^(2) vec b lambda vec c] = [ vec a vec b + vec c vec b]` for

A

exactly two values of `lambda`

B

actly three values of `lambda`

C

no value of `lambda`

D

exactly one values of `lambda`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|194 Videos

Similar Questions

Explore conceptually related problems

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

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| =

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

If vec a, vec b, vec c non zero coplanar vectors, then, [2 vec a - vec b 3 vec b - vec c 4 vec c - vec a] =

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

If vec a, vec b, vec c are linearly independent vectors and Delta = |(vec a, vec b, vec c), (vec a. vec a, vec a.vec b, veca . vec c), (vec a. vec c, vec b . vecc, vec c. vec c)| then ,

Let vec a, vec b and vec c are unit coplanar vectors then the scalar triple product [2 vec a - vec b 2 vec b - vec c 2 vec c - vec a]

If vec a, vec b, vec c are three vectors such that vec a + vec b + vec c = vec 0 and |vec a| = 2, |vec b| = 3, |vec c| = 5 , then the value of vec a . vec b + vec b . vec c + 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| =

HIMALAYA PUBLICATION-VECTORS AND THEIR APPLICATIONS-QUESTION BANK
  1. The values of 'a' for which the points A, B, C with position vectors 2...

    Text Solution

    |

  2. If the vector veca = hati + ahatj + a^(2) hatk , vecb = hati + b hatj ...

    Text Solution

    |

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

    Text Solution

    |

  4. Let vec a = i +j + k, vec b = i-j+2k, vec c = x i+(x-2)j-k. If the vec...

    Text Solution

    |

  5. The non-zero vectors vec b and vec c are related by vec a = 8 vec b an...

    Text Solution

    |

  6. The vectors vec a = alpha i +2j+betak lies in the plane of the vectors...

    Text Solution

    |

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

    Text Solution

    |

  8. If vec a = j-k and vec c = i-j-k. Then the vector vec b satisfying vec...

    Text Solution

    |

  9. If the vectors vec a = i-j+2k, vec b = 2i+4j+k and vec c = lambda i + ...

    Text Solution

    |

  10. If vec a and vec b are not perpendicular to each other and vec r xx ve...

    Text Solution

    |

  11. If vec a = 1/sqrt10 (3i+k) and vec b = 1/7 (2i+3j-6k) then the value o...

    Text Solution

    |

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

    Text Solution

    |

  13. For any three vectors vec a, vec b, vec c the expression (vec a - vec ...

    Text Solution

    |

  14. For any vector vec r, the value of i xx (vec r xx i) + j xx (vec r xx...

    Text Solution

    |

  15. Let the unit vectors vec a and vec b be perpendicular to each other an...

    Text Solution

    |

  16. If the points P(vec a + 2 vec b + vec c), Q (2 vec a + 3 vec b), R(vec...

    Text Solution

    |

  17. If vec a, vec b, vec c are three mutually perpendicular vectors of equ...

    Text Solution

    |

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

    Text Solution

    |

  19. If the vectors vec r(1) = ai+j+k, vec r(2) = i + bj + k, vec r(3) = i ...

    Text Solution

    |

  20. A unit vector in the xy plane that makes an angle of 45^(o) with the v...

    Text Solution

    |