Home
Class 12
MATHS
If vecr=x(1)(vecaxx vecb) + x(2) (vecb x...

If `vecr=x_(1)(vecaxx vecb) + x_(2) (vecb xxveca) + x_(3)(vecc xxvecd) and 4[veca vecb vecc] =1 " then " x_(1) + x_(2) + x_(3)` is equal to

A

`1/2vecr.(veca + vecb + vecc)`

B

`1/4vecr.(veca + vecb + vecc)`

C

`2vecr.(veca + vecb + vecc)`

D

`4vecr.(veca + vecb + vecc)`

Text Solution

Verified by Experts

The correct Answer is:
d
`vecr= x_(1)(vecaxx vecb) + x_(2)(vecb xx vecc)+x_(3)(vecc xxveca)`
`Rightarrow vecr.veca=x_(2)[veca vecb vecc] . vecr.vecb=x_(3)[vecb vecc veca]`
` and vecr.vecc= x_(1)[vecc veca vecb] =x_(1) [vecb vecc veca]`
` Rightarrow x_(1)+x_(2)+x_(3)=4vecr. (veca +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 vecr=x(vecaxxvecb)+y(vecbxxvecc)+z(veccxxveca) and [veca vecb vecc]=(1)/(3) , then x+y+z is equal to

If [veca xx vecb vecb xx vecc vecc xx veca]=lambda[veca vecb vecc^(2)] , then lambda is equal to

If vecr=x(vecaxxvecb)+y(vecbxxvecc)+z(vecc+veca) Such that x+y+z!=0 and vecr.(veca+vecb+vecc)=x+y+z , then [veca vecb vecc]=

If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc + vecc xx veca=

If vecr=x(vecaxxvecb)+y(vecbxxvecc)+z(veccxxveca) such that x+y+z!=0 and vecr.(veca+vecb+vecc)=x+y+z, then [[veca,vecb, vecc]]=

For three non - zero vectors veca, vecb and vecc , if [(veca, vecb , vecc)]=4 , then [(vecaxx(vecb+2vecc), vecbxx(vecc-3veca), vecc xx(3veca+vecb))] is equal to

Prove that veca\'xxvecb\'+vecb\'xxvecc\'+vecc\'xxveca\'=(veca+vecb+vecc)/([veca vecb vecc])

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If V be the volume of a tetrahedron and V ' be the volume of anothe...

    Text Solution

    |

  2. [(veca xxvecb)xx(vecb xx vecc) (vecb xxvecc) xx (vecc xxveca) (veccxxv...

    Text Solution

    |

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

    Text Solution

    |

  4. If the vectors veca and vecb are perpendicular to each other then a ve...

    Text Solution

    |

  5. If veca,' = hati + hatj, vecb'= hati - hatj + 2hatk nad vecc' = 2hati ...

    Text Solution

    |

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

    Text Solution

    |

  7. If unit vectors veca and vecb are inclined at an angle 2 theta such th...

    Text Solution

    |

  8. vecb and vecc are non- collinear if veca xx (vecb xx vecc) + (veca .ve...

    Text Solution

    |

  9. Unit vectors veca and vecb ar perpendicular , and unit vector vecc is ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |