Home
Class 12
MATHS
If vec axx( vec bxx vec c) is perpendic...

If ` vec axx( vec bxx vec c)` is perpendicular to `( vec axx vec b)xx vec c ,` we may have a.`( vec a . vec c)| vec b|^2=( vec a . vec b)( vec b . vec c)` b. ` vec adot vec b=0` c. ` vec adot vec c=0` d. ` vec bdot vec c=0`

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 All Questions|268 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

Similar Questions

Explore conceptually related problems

If vec a , vec ba n d vec c are non coplanar vectors and vec axx vec c is perpendicular to vec axx( vec bxx vec c), then the value of [axx( vec bxx vec c)]xx vec c is equal to a. [ vec a vec b vec c] b. 2[ vec a vec b vec c] vec b c. vec0 d. [ vec a vec b vec c] vec a

Prove that vec a xx (vec b + vec c) + vec b xx(vec a + vec c)+ vec c xx(vec a + vec b) = vec 0

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=0

If [ vec a vec b vec c]=2, then find the value of [( vec a+2 vec b- vec c)( vec a- vec b)( vec a- vec b- vec c)]dot

For any three vectors veca, vec b, vec c prove that (vec a + vec b)+ vec c = vec a + (vec b + vec c)

If vec a is parallel to vec bxx vec c , then ( vec axx vec b)dot( vec axx vec c) is equal to a. | vec a|^2( vec b . vec c) b. | vec b|^2( vec a . vec c) c. | vec c|^2( vec a . vec b) d. none of these

The condition for equations vec rxx vec a= vec ba n d vec rxx vec c= vec d to be consistent is a. vec b . vec c= vec a . vec d b. vec a . vec b= vec c .vec d c. vec b . vec c+ vec a . vec d=0 d. vec adot vec b+ vec c .vec d=0

If vec a+2 vec b+3 vec c=0,t h e n vec axx vec b+ vec bxx vec c+ vec cxx vec a= 2( vec axx vec b) b. 6( vec bxx vec c) c. 3( vec cxx vec a) d. vec0

Value of [ vec axx vec b vec axx vec c vec d] is always equal to ( vec a . vec d)[ vec a vec b vec c] b. ( vec a . vec c)[ vec a vec b vec d] c. ( vec a . vec b)[ vec a vec b vec d] d. none of these

If vec aa n d vec b are two vectors, then prove that ( vec axx vec b)^2=| vec adot vec a vec adot vec b vec bdot vec a vec bdot vec b| .

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

    Text Solution

    |

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

    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 are two given perpendicular vectors, which are non-z...

    Text Solution

    |

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

    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 side vec A B of an equilateral trangle A B C lying in the x-y plan...

    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

    |