Home
Class 11
MATHS
If (veca xxv vecb) xx (vecc xx vecd) . (...

If `(veca xxv vecb) xx (vecc xx vecd) . (veca xx vecd) =0` then which of the following may be true ?

A

`veca, vecb and vecd` are nenessarily coplanar

B

`veca` lies iin the plane of `vecc and vecd`

C

`vecvb` lies in the plane of `veca and vecd`

D

`vecc` lies in the plane of `veca and vecd`

Text Solution

Verified by Experts

The correct Answer is:
b,c,d
`(vecaxxvecb )xx(vecc xx vecd). (vecaxxvecd) =0`
`or ([veca vecc vecd] vecb- [vecb vecc vecd]veca) . (veca xx vecd)=0`
`or [veca veccvecd] [vecb veca vecd] =0`
Hence, either `vecc or vecb` must lie in the plane of ` veca and vecd`.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise JEE Previous Year (Single Question)|28 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise JEE Previous Year (Multiple Question)|11 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise 2.3|18 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|1316 Videos

  • LIMITS AND DERIVATIVES

    CENGAGE|Exercise Solved Examples And Exercises|320 Videos

Similar Questions

Explore conceptually related problems

If alpha(veca xx vecb)+beta(vecb xx vecc)+lambda(vecc xx veca)=0 , then

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,vecb,vecd,vecd be vectors such that [vecavecbvecc]=2 and (vecaxxvecb) xx (vecc xx vecd)+(vecb xx vecc) xx (vecc xx vecd) + (vecc xx veca) xx (vecb xx vecd)=-muvecd Then the value of mu is

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:

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

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

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

If (veca xx vecb) xx (vec c xx vecd)=h veca+k vecb=r vec c+s vecd , where veca, vecb are non-collinear and vec c, vec d are also non-collinear then :

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. [vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to

    Text Solution

    |

  2. The scalars l and m such that lveca + m vecb =vecc, " where " veca, ve...

    Text Solution

    |

  3. If (veca xxv vecb) xx (vecc xx vecd) . (veca xx vecd) =0 then which of...

    Text Solution

    |

  4. A,B C and dD are four points such that vec (AB) = m(2 hati - 6 hatj +...

    Text Solution

    |

  5. If the vectors veca, vecb, vecc are non -coplanar and l,m,n are distin...

    Text Solution

    |

  6. Let vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk and vec(...

    Text Solution

    |

  7. If vectors vecA=2hati+3hatj+4hatk, vecB=hati+hatj+5hatk and vecC form ...

    Text Solution

    |

  8. If veca=xhati + y hatj + zhatk, vecb= yhati + zhatj + xhatk and vecc= ...

    Text Solution

    |

  9. If veca xx (vecbxx vecc)= (veca xx vecb)xxvecc then

    Text Solution

    |

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

    Text Solution

    |

  11. A parallelogram is constructed on the vectors veca=3vecalpha-vecbeta, ...

    Text Solution

    |

  12. <b>Statement 1:</b> Vector vecc = -5hati + 7 hatj + 2hatk is along th...

    Text Solution

    |

  13. Statement1: A component of vector vecb = 4hati + 2hatj + 3hatk in the ...

    Text Solution

    |

  14. Statement 1: Distance of point D( 1,0,-1) from the plane of points A( ...

    Text Solution

    |

  15. Let vecr be a non - zero vector satisfying vecr.veca = vecr.vecb =vecr...

    Text Solution

    |

  16. Statement 1: If a(1)hati + a(2)hatj + a(3)hatk, vecb(1)hati+b(2)hatj +...

    Text Solution

    |

  17. Statement 1: vecA=2hati + 3hatj + 6hatk , vecB=hati + hatj - 2hatk and...

    Text Solution

    |

  18. Statement 1: veca, vecb and vecc arwe three mutually perpendicular uni...

    Text Solution

    |

  19. Consider three vectors veca , vecb and vecc Statement 1: vecaxxvecb ...

    Text Solution

    |

  20. Let vecu, vecv and vecw be three unit vectors such that vecu + vecv + ...

    Text Solution

    |