Home
Class 12
MATHS
If vecca xx (vec b xx vecc) is perpendic...

If `vecca xx (vec b xx vecc)` is perpendicular to `(veca xx vecb ) xx vecc`, we may have

A

`(veca.vecb)|vecb|^(2)= (veca.vecb)(vecb.vecc)`

B

`veca.vecb=0`

C

`veca.vecc=0`

D

`vecb.vecc=0`

Text Solution

Verified by Experts

The correct Answer is:
a,c
`vecaxx(vecbxxvecc)= (veca.vecc)vecb-(veca.vecb)vecb]and (vecaxx vecb) xxvecc=-(vecc. vecb) veca + (veca.vecc)vecb`
we have been givn
`(veca xx (vecbxx vecc)). ((vecaxxvecb)xxvecc)=0`
` or (veca . vecc)^(2)|vecb|^(2)- (veca.vecc)(vecb.vecc) (veca.vecb)`
` - (veca.vecb) (veca.vecc)(vecb.vecc)+ (veca.vecb)(vecb.vecc)(vecc.veca)=0`
`or (veca.vecc)^(2)|vecb|^(2)= (veca.vecc)(veca.vecb)(vecb.vecc)`
`or (veca.vecc)((veca.vecc)(vecb.vecb)- (veca.vecb) (vecb.vecc))=0`
`veca.veca=0 or (veca.vecc) |vecb|^(2) = (veca.vecb)(vecb.vecc)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

  • DETERMINANTS

    CENGAGE|Exercise Question Bank|23 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|25 Videos

Similar Questions

Explore conceptually related problems

If veca xx (vecb xx vecc) is perpendicular to (veca xx vecb) xx vecc , then we may have:

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

Let veca,vecb,vecc be three non coplanar and vecd be a vector which is perpendicular to veca + vecb + vecc . If vecd = xvecb xx vecc + yvecc xx veca + zveca xx vecb the-

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

Let veca vecb and vecc be non- zero vectors aned vecV_(1) =veca xx (vecb xx vecc) and vecV_(2) = (veca xx vecb) xx vecc .vectors vecV_(1) and vecV_(2) are equal . Then

If (veca xx vecb) xx vecc = vec a xx (vecb xx vecc) , where veca, vecb and vecc are any three vectors such that veca.vecb ne 0, vecb.vecc ne 0 , then veca and vecc are:

If (veca xx vecb) xx vecc = veca xx (vecb xx vecc) where veca, vecb and vecc are any three vectors such that veca.vecb =0, vecb.vecc=0 then veca and vecc are:

veca=2hati+hatj+2hatk, vecb=hati-hatj+hatk and non zero vector vecc are such that (veca xx vecb) xx vecc = veca xx (vecb xx vecc) . Then vector vecc may be given as

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 .

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Unit vectors veca and vecb ar perpendicular , and unit vector vecc is ...

    Text Solution

    |

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

    Text Solution

    |

  3. If vecca xx (vec b xx vecc) is perpendicular to (veca xx vecb ) xx vec...

    Text Solution

    |

  4. If vecp=(vecbxxvecc)/([(veca,vecb,vecc)]),vecq=(veccxxveca)/([(veca,ve...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. Let veca and vecb be two non- zero perpendicular vectors. A vector vec...

    Text Solution

    |

  8. If vector vec b=(t a nalpha,-12sqrt(sinalpha//2))a n d vec c=(t a nal...

    Text Solution

    |

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

    Text Solution

    |

  10. If veca and vecb are unequal unit vectors such that (veca - vecb) xx[ ...

    Text Solution

    |

  11. If veca and vecb are two unit vectors perpenicualar to each other and ...

    Text Solution

    |

  12. If vectors veca and vecb are non collinear then veca/(|veca|)+vecb/(|v...

    Text Solution

    |

  13. If veca and vecb are non - zero vectors such that |veca + vecb| = |vec...

    Text Solution

    |

  14. Let veca vecb and vecc be non- zero vectors aned vecV(1) =veca xx (vec...

    Text Solution

    |

  15. Vectors vecA and vecB satisfying the vector equation vecA+ vecB = vec...

    Text Solution

    |

  16. A vector vecd is equally inclined to three vectors veca=hati-hatj+hatk...

    Text Solution

    |

  17. Vectors perpendicular tohati-hatj-hatk and in the plane of hati+hatj+h...

    Text Solution

    |

  18. If the sides vec(AB) of an equilateral triangle ABC lying in the xy-pl...

    Text Solution

    |

  19. Let hata be a unit vector and hatb a non zero vector non parallel to v...

    Text Solution

    |

  20. veca ,vecb and vecc are unimdular and coplanar. A unit vector vecd is ...

    Text Solution

    |