Home
Class 12
MATHS
For any four vectors prove that (vecbx...

For any four vectors prove that
`(vecbxxvecc).(veca xxvecd)+(vecc xxveca).(vecbxxvecd)+(vecaxxvecb).(veccxxvecd)=0`

Text Solution

Verified by Experts

`(vecbxxvecc).(vecaxxvecd)=(vecb.veca)(vecc.vecd)-(vecb.vecd)(vecc.veca)`
`(veccxxveca).(vecbxxvecd)=(vecc.vecd)(veca.vecd)-(vecc.vecd)(veca.vecb)`
`(vecaxxvecb).(veccxxvecd)+(veca.vecc)(vecb.vecd)-(veca.vecd)(vecb.vecc)`
`Rightarrow (vecbxxvecc).(vecaxxvecd)+(veccxxveca).(vecbxxvecd)+(vecaxxvecb).(vecc xxvec)=0`
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

Prove that: (vecb xx vecc).(vecaxxvecd)+(veccxxveca).(vecbxxvecd)+(vecaxxvecb).(veccxxvecd)=0

Prove that (vecbxxvecc)xx(veccxxveca)=[veca vecb vecc]vecc

If veca+vecb+vecc=0 , prove that (vecaxxvecb)=(vecbxxvecc)=(veccxxveca)

For any three vectors veca,vecb,vecc their product would be a vector if one cross product is folowed by other cross product i.e (vecaxxvecb)xxvecc or (vecbxxvecc)xxveca etc. For any four vectors veca,vecb,vecc,vecd the product would be a vector with the help of sequential cross product or by cross product of two vectors obtained by corss product of two pair i.e. (vecaxx(vecbxxvecc))xxvecd or (vecaxxvecb)xx(veccxxvecd). (vecaxxvecb)xx(veccxxvecd0 is a vector (A) along the line off intersection of two planes containing veca,vecb and vecc,vecd (B) perpendicular to plane containing veca,vecb and vecc,vecd (C) parallel to the plane containing veca,vecb and vecc,vecd (D) none of these

For vectors veca,vecb,vecc,vecd, vecaxx(vecbxxvecc)=(veca.vecc)vecb-(veca.vecb)vecc and (vecaxxvecb).(veccxxvecd)=(veca.vecc)(vecb.vecd)(veca.vecd)(vecb.vecc) Now answer the following question: (vecaxxvecb).(vecxxvecd) is equal to (A) (vecaxxvecd).(vecbxxvecc) (B) (vecbxxveca).(veccxxvecd) (C) (vecdxxvecc).(vecbxxveca0 (D) none of these

For vectors veca,vecb,vecc,vecd, vecaxx(vecbxxvecc)=(veca.vecc)vecb-(veca.vecb)vecc and (vecaxxvecb).(veccxxvecd)=(veca.vecc)(vecb.vecd)(veca.vecd)(vecb.vecc) Now answer the following question: (vecaxxvecb).(vecxxvecd) is equal to (A) veca.(vecbxx(vecxxvecd)) (B) |veca|(vecb.(veccxxvecd)) (C) |vecaxxvecb|.|veccxxvecdD| (D) none of these

For vectors veca,vecb,vecc,vecd, vecaxx(vecbxxvecc)=(veca.vecc)vecb-(veca.vecb)vecc and (vecaxxvecb).(veccxxvecd)=(veca.vecc)(vecb.vecd)(veca.vecd)(vecb.vecc) Now answer the following question: {(vecaxxvecb).xxvecc}.vecd would be equal to (A) veca.(vecxx(veccxxvecd)) (B) ((vecaxxvecc)xxvecb).vecd (C) (vecaxxvecb).(vecdxxvecc) (D) none of these

If veca, vecba and vecc are non- coplanar vecotrs, then prove that |(veca.vecd)(vecbxxvecc)+(vecb.vecd)(veccxxveca)+(vecc.vecd)(vecaxxvecb) is independent of vecd where vecd is a unit vector.

If veca, vecba and vecc are non- coplanar vecotrs, then prove that |(veca.vecd)(vecbxxvecc)+(vecb.vecd)(veccxxveca)+(vecc.vecd)(vecaxxvecb) is independent of vecd where vecd is a unit vector.

for any four vectors veca,vecb, vecc and vecd prove that vecd. (vecaxx(vecbxx(veccxxvecd)))=(vecb.vecd)[veca vecc vecd]

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. For any four vectors prove that (vecbxxvecc).(veca xxvecd)+(vecc xxv...

    Text Solution

    |

  2. Find |veca| and |vecb| if (veca+vecb).(veca-vecb)=8 and |veca|=8|vecb|...

    Text Solution

    |

  3. Show that |veca|vecb+|vecb|veca is perpendicular to |veca|vecb-|vecb|v...

    Text Solution

    |

  4. If the vectors A ,B ,C of a triangle A B C are (1,2,3),(-1,0,0),(0,1,2...

    Text Solution

    |

  5. If |veca|=3, |vecb|=4 and the angle between veca and vecb is 120^(@) ....

    Text Solution

    |

  6. If vectors hati-2xhatj-3yhatk and hati+ 3 x hatj + 2yhatk are orthogon...

    Text Solution

    |

  7. Let veca vecb and vecc be pairwise mutually perpendicular vectors, suc...

    Text Solution

    |

  8. If veca +vecb +vecc=0, |veca|=3,|vecb|=5, |vecc|=7 , then find the ang...

    Text Solution

    |

  9. If the angle between unit vectors veca and vecb is 60^(@) . Then find ...

    Text Solution

    |

  10. Let vecu=hai+hatj,vecv=hati-hatj and vecw=hati+2hatj+3hatk. If hatn is...

    Text Solution

    |

  11. A , B , C , D are any four points, prove that vec A Bdot vec C D+ ...

    Text Solution

    |

  12. P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(,-2,-1), then find the projection...

    Text Solution

    |

  13. If the vectors 3vecP+vecq, 5vecP - 3vecq and 2 vecp+ vecq, 4 vecp - 2v...

    Text Solution

    |

  14. Let vecA and vecB be two non-parallel unit vectors in a plane. If (alp...

    Text Solution

    |

  15. Let veca , vecb and vecc be unit vectors such that veca+vecb+vecc=vecx...

    Text Solution

    |

  16. If veca and vecb are unit vectors, then find the greatest value of |ve...

    Text Solution

    |

  17. Constant forces P(1)=hati-hatj+hatk, P(2)= -hati+2hatj-hatik and P(3)=...

    Text Solution

    |

  18. Find |veca| and |vecb| if (veca+vecb).(veca-vecb)=8 and |veca|=8|vecb|...

    Text Solution

    |

  19. If A ,B ,C ,D are four distinct point in space such that A B is not...

    Text Solution

    |

  20. If veca=2hati+ 3hatj-5hatk,vecb =m hati+nhatj +12 hatk and veca xx vec...

    Text Solution

    |

  21. Find veca.vecb if |veca|2, |vecb|=5,a and |vecaxxvecb|=8

    Text Solution

    |