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

If `vecr=x_(1)(vecaxx vecb) + x_(2) (vecb xxvecc) + x_(3)(vecc xxveca) 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 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 xx (vecbxx vecc)= (veca xx vecb)xxvecc then

[vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to

Prove that [veca+vecb vecb+vecc vecc+veca]=2[veca vecb vecc]

If veca, vecb, vecc and vecd are unit vectors such that (vecaxx vecb).(veccxxvecd)=1 and veca.vecc=1/2 then

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

Let veca vecb and vecc be non- zero vectors aned vecV_(1) =veca xx (vecb xx vecc) and vecV_(2) = (veca xx vecb) xx vecc .vectors vecV_(1) and vecV_(2) are equal . Then

If veca,vecb and vecc are three non coplanar vectors and vecr is any vector in space, then (vecaxxvecb)xx(vecrxxvecc)+(vecb xxvecc)xx(vecrxxveca)+(veccxxveca)xx(vecrxxvecb)= (A) [veca vecb vecc] (B) 2[veca vecb vecc]vecr (C) 3[veca vecb vecc]vecr (D) 4[veca vecb vecc]vecr

If veca , vecb and vecc are non- coplanar vectors and veca xx vecc is perpendicular to veca xx (vecb xx vecc) , then the value of [ veca xx ( vecb xx vecc)] xx vecc is equal to

If |veca xx vecb|=3 and veca*vecb=4 , then the value of |veca|^(2)|vecb|^(2) is -

If [ veca vecbvecc]=2 , then find the value of [(veca+2vecb-vecc) (veca - vecb) (veca - vecb-vecc)]

CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. If V be the volume of a tetrahedron and V ' be the volume of another...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. If unit vectors vec a and vec b are inclined at angle 2theta such t...

    Text Solution

    |

  8. vec a, vec ba n d vec c are non-collinear if vec axx( vec bxx vec c)+...

    Text Solution

    |

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

    Text Solution

    |

  10. If vectors vec aa n d vec b are two adjacent sides of a parallelogr...

    Text Solution

    |

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

    Text Solution

    |

  12. Let vec a , vec b ,a n d vec c be vectors forming right-hand traid. L...

    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 vec aa n d vec b are two vectors and angle between them is thet...

    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,-1, 2sqrt(sinalpha//2))a n d vec c=(t a n...

    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

    |