Home
Class 12
MATHS
If vecr.veca=vecr.vecb=vecr.vecc=0 " whe...

If `vecr.veca=vecr.vecb=vecr.vecc=0 " where "veca,vecb and vecc` are non-coplanar, then

A

`vecrbot(veccxxveca)`

B

`vecrbot(vecaxxvecb)`

C

`vecrbot(vecbxxvecc)`

D

`vecr=vec0`

Text Solution

Verified by Experts

The correct Answer is:
d
Let `vecr ne vec0` then `vecr.veca = vecr.vecb = vecr.vecc =0`
Hence, `veca, vecb and vecc` are coplanar, which is a contradiction.
Therefore, `vecr =vec0`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

  • DETERMINANTS

    CENGAGE|Exercise All Questions|268 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

Similar Questions

Explore conceptually related problems

If vecP = (vecbxxvecc)/([vecavecbvecc]),vecq=(veccxxveca)/([veca vecb vecc])and vecr = (vecaxxvecb)/([veca vecbvecc]), " where " veca,vecb and vecc are three non- coplanar vectors then the value of the expression (veca + vecb + vecc ). (vecp+ vecq+vecr) is

If veca xx vecb = vecb xx vecc ne 0 where veca , vecb and vecc are coplanar vectors, then for some scalar k prove that veca+vecc = kvecb .

If vecr.veca=vecr.vecb=vecr.vecc=1/2 for some non zero vector vecr and veca,vecb,vecc are non coplanar, then the area of the triangle whose vertices are A(veca),B(vecb) and C(vecc0 is (A) |[veca vecb vecc]| (B) |vecr| (C) |[veca vecb vecr]vecr| (D) none of these

Let vecr be a non - zero vector satisfying vecr.veca = vecr.vecb =vecr.vecc =0 for given non- zero vectors veca vecb and vecc Statement 1: [ veca - vecb vecb - vecc vecc- veca] =0 Statement 2: [veca vecb vecc] =0

Let vecr = (veca xx vecb)sinx + (vecb xx vecc)cosy+(vecc xx veca) , where veca,vecb and vecc are non-zero non-coplanar vectors, If vecr is orthogonal to 3veca + 5vecb+2vecc , then the value of sec^(2)y+"cosec"^(2)x+secy" cosec "x is

Show that the vectors 2veca-vecb+3vecc, veca+vecb-2vecc and veca+vecb-3vecc are non-coplanar vectors (where veca, vecb, vecc are non-coplanar vectors).

If vecx.veca=0 , vecx.vecb=0 , vecx.vecc=0 and vecxnevec0 then show yhat veca , vecb , vecc are coplanar .

if veca xx vecb = vecc,vecb xx vecc = veca , " where " vecc ne vec0 then

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If hata,hatb and hatc are three unit vectors inclined to each other at...

    Text Solution

    |

  2. Let the pair of vector veca,vecb and vecc,vecd each determine a plane....

    Text Solution

    |

  3. If vecr.veca=vecr.vecb=vecr.vecc=0 " where "veca,vecb and vecc are non...

    Text Solution

    |

  4. If veca satisfies vecaxx(hati+2hatj+hatk)=hati-hatk" then " veca is eq...

    Text Solution

    |

  5. Vectors 3veca-5vecb and 2veca + vecb are mutually perpendicular. If ve...

    Text Solution

    |

  6. The units vectors orthogonal to the vector - hat i + 2hat j + 2hat k ...

    Text Solution

    |

  7. The value of x for which the angle between veca=2x^(2)hati+4xhatj + ha...

    Text Solution

    |

  8. If vectors veca and vecb are two adjacent sides of parallelograsm then...

    Text Solution

    |

  9. A parallelogram is constructed on 3 vec a+ vec ba n d vec a-4 vec b ...

    Text Solution

    |

  10. Let veca.vecb=0 where veca and vecb are unit vectors and the vector ve...

    Text Solution

    |

  11. veca and vecc are unit vectors and |vecb|=4 the angle between veca and...

    Text Solution

    |

  12. Let the position vectors of the points Pa n dQ be 4 hat i+ hat j+la...

    Text Solution

    |

  13. A vector of magnitude sqrt2 coplanar with the vectors veca=hati+hatj+2...

    Text Solution

    |

  14. Let P be a point interior to the acute triangle A B Cdot If P A+P B...

    Text Solution

    |

  15. G is the centroid of triangle A B Ca n dA1a n dB1 are rthe midpoint...

    Text Solution

    |

  16. Points vec a , vec b , vec c ,a n d vec d are coplanar and (s inalpha...

    Text Solution

    |

  17. If veca and vecb are any two vectors of magnitudes 1and 2. respectivel...

    Text Solution

    |

  18. If vec aa n d vec b are any two vectors of magnitudes 2 and 3, resp...

    Text Solution

    |

  19. veca, vecb and vecc are unit vecrtors such that |veca + vecb+ 3vecc|=4...

    Text Solution

    |

  20. If the vector product of a constant vector vec O A with a variable...

    Text Solution

    |