Home
Class 12
MATHS
If veca and vecb are othogonal unit vect...

If `veca and vecb` are othogonal unit vectors, then for a vector `vecr` non - coplanar with `veca and vecb` vector `vecr xx veca` is equal to

A

`[vecr vecavecb]vecb - (vecr.vecb)(vecbxxveca)`

B

`[vecrvecavecb] (veca+vecb)`

C

`[vecr vecavecb]veca + (vecr.veca) vecaxxvecb`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
`vecr xxveca =lambdaveca + muvecb +gammavecaxxvecb`
`[vecr veca veca]=lamdaveca.veca+muvecb.veca+vecgamma[veca vecb veca]`
`0 = lamda|veca|^(2) +0+0`
`lamda=0`
Also ` [vecr vecavecb] = lamdaveca.vecb+ muvecb .vecb+ gamma[veca vecb vecb]=mu`
Also `(vecrxxveca) xxvecb=gamma(veca xxvecb) xxvecb`
`or (vecr.vecb)veca= -gammavecaor gamma= -(vecr.vecb)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Reasoning type|8 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Comprehension type|27 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercises|15 Videos

  • DETERMINANTS

    CENGAGE PUBLICATION|Exercise All Questions|262 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

Similar Questions

Explore conceptually related problems

If veca and vecb are unit vectors, then angle between veca and vecb for sqrt3 ​ veca − vec b to be unit vector is

If vecb and vecc are unit vectors, then for any arbitary vector veca, (((veca xx vecb) + (veca xx vecc))xx (vecb xx vecc)) .(vecb -vecc) is always equal to

If vec a \ a n d \ vec b are two non-collinear unit vector, and ∣ ​ veca + vecb ∣ ​ = 3 ​ then (2 veca −5 vecb ).(3 veca + vecb ) =

If vectors veca and vecb are non collinear then veca/(|veca|)+vecb/(|vecb|) is

If veca and vecb are non - zero vectors such that |veca + vecb| = |veca - 2vecb| then

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 and vecb are unit vectors, then find the greatest value of |veca+vecb|+ |veca-vecb| .

If vec a , vec ba n d vec c are three non coplanar vectors, then ( veca + vecb + vecc )[( veca + vecb )×( veca + vecc )] is :

CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. A vector of magnitude 10 along the normal to the curve 3x^2+8x y+2y...

    Text Solution

    |

  2. If vec aa n d vec b are two unit vectors incline at angle pi//3 , ...

    Text Solution

    |

  3. If veca and vecb are othogonal unit vectors, then for a vector vecr no...

    Text Solution

    |

  4. If veca,vecb ,vecc are any three non- coplanar vectors then the equa...

    Text Solution

    |

  5. Solve the simultaneous vector equations for vecx and vecy: vecx+veccxx...

    Text Solution

    |

  6. The condition for equations vec rxx vec a= vec ba n d vec rxx vec c...

    Text Solution

    |

  7. If veca=2hati+3hatj+hatk, vecb=hati-2hatj+hatk and vecc=-3hati+hatj+2h...

    Text Solution

    |

  8. If veca=2hati + 3hatj+ 8hatk is perpendicular to vecb= 4hati-4hatj + a...

    Text Solution

    |

  9. Let veca (x) = (sin x) hati+ (cos x) hatj and vecb(x) = (cos 2x) hati ...

    Text Solution

    |

  10. For any vectors veca and vecb, (veca xx hati) . (vecb xx hati) + ( vec...

    Text Solution

    |

  11. If veca,vecb and vecc are three non coplanar vectors and vecr is any v...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. [( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)(...

    Text Solution

    |

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

    Text Solution

    |

  18. If veca bot vecb then vector vecv in terms of veca and vecb satisfying...

    Text Solution

    |

  19. If vec a^'= hat i+ hat j , vec b^' hat i- hat j+2 hat ka n d vec c^'2...

    Text Solution

    |

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

    Text Solution

    |