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

If `veca , vecb and vecc` are non- coplanar vectors and `veca xx vecc` is perpendicular to `veca xx (vecb xx vecc)` , then the value of `[ veca xx ( vecb xx vecc)] xx vecc` is equal to

A

` [veca vecb vecc] vecc`

B

`[ veca vecb vecc] vecb`

C

` vec0`

D

`[veca vecb vecc] veca`

Text Solution

Verified by Experts

The correct Answer is:
c
Given that `veca, vecb and vecc` are non-coplanar, thus
` [veca vecb vecc] ne 0`
again ` veca xx (vecb xx vecc) . (veca xx vecc) =0`
`or (veca .vecc) =0`
Hence, ` veca and vecc` are perpendicular,
` veca xx (vecb xx vecc) = (veca .vecc) vecb - (veca .vecb) vecc`
` or [veca xx (vecb xx vecc)] xx vecc = 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

Let veca, vecb, and vecc be three non- coplanar vectors and vecd be a non -zero , which is perpendicular to (veca + vecb + vecc). Now vecd = (veca xx vecb) sin x + (vecb xx vecc) cos y + 2 (vecc xx veca) . Then

If veca, vecb and vecc 1 are three non-coplanar vectors, then (veca + vecb + vecc). [(veca + vecb) xx (veca + vecc)] equals

If veca is parallel to vecb xx vecc, then (veca xx vecb) .(veca xx vecc) is equal to

If vectors, vecb, vcec and vecd are not coplanar, the pove that vector (veca xx vecb) xx (vecc xx vecd) + ( veca xx vecc) xx (vecd xx vecb) + (veca xx vecd) xx (vecb xx vecc) is parallel to veca .

If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc + vecc xx veca=

Let veca, vecb , vecc be non -coplanar vectors and let equations veca', vecb', vecc' are reciprocal system of vector veca, vecb ,vecc then prove that veca xx veca' + vecb xx vecb' + vecc xx vecc' is a null vector.

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

If veca, vecb and vecc are unit coplanar vectors , then the scalar triple porduct [2 veca -vecb" " 2vecb - vecc " "2vecc-veca] is

If veca, vecb and vecc are three non-coplanar non-zero vectors, then prove that (veca.veca) vecb xx vecc + (veca.vecb) vecc xx veca + (veca.vecc)veca xx vecb = [vecb vecc veca] veca

If veca, vecb,vecc are unit vectors such that veca.vecb = 0= veca.vecc and the angle between vecb and vecc is pi//3 then the value of |vecaxxvecb -veca xx vecc| is

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If vecP = (vecbxxvecc)/([vecavecbvecc]),vecq=(veccxxveca)/([veca vecb ...

    Text Solution

    |

  2. A (veca), B (vecb) and C (vecc) are the vertices of triangle ABC and R...

    Text Solution

    |

  3. If veca , vecb and vecc are non- coplanar vectors and veca xx vecc is ...

    Text Solution

    |

  4. If V be the volume of a tetrahedron and V ' be the volume of another...

    Text Solution

    |

  5. [(veca xxvecb)xx(vecb xx vecc) (vecb xxvecc) xx (vecc xxveca) (veccxxv...

    Text Solution

    |

  6. If vecr=x(1)(vecaxx vecb) + x(2) (vecb xxvecc) + x(3)(vecc xxveca) and...

    Text Solution

    |

  7. If the vectors veca and vecb are perpendicular to each other then a ve...

    Text Solution

    |

  8. If veca' = hati + hatj, vecb'= hati - hatj + 2hatk nad vecc' = 2hati -...

    Text Solution

    |

  9. If veca= hati +hatj, vecb= hatj + hatk, vecc = hatk + hati then in th...

    Text Solution

    |

  10. If unit vectors veca and vecb are inclined at an angle 2 theta such th...

    Text Solution

    |

  11. Differentiate y=cos^4 4x

    Text Solution

    |

  12. Unit vectors veca and vecb ar perpendicular , and unit vector vecc is ...

    Text Solution

    |

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

    Text Solution

    |

  14. If vec axx( vec bxx vec c) is perpendicular to ( vec axx vec b)xx vec...

    Text Solution

    |

  15. If vecP = (vecbxxvecc)/([vecavecbvecc]),vecq=(veccxxveca)/([veca vecb ...

    Text Solution

    |

  16. a(1), a(2),a(3) in R - {0} and a(1)+ a(2)cos2x+ a(3)sin^(2)x=0 " for ...

    Text Solution

    |

  17. If veca and vecb are two vectors and angle between them is theta , the...

    Text Solution

    |

  18. Let veca and vecb are two given perpendicular vectors, which are non-z...

    Text Solution

    |

  19. If vectors vecb= (tan alpha, -1,2 sqrtsinalpha//2)and vecc= (tanalpha,...

    Text Solution

    |

  20. Let vecr be a unit vector satisfying vecr xx veca = vecb, " where " |v...

    Text Solution

    |