Home
Class 12
MATHS
If the vectors veca, vecb, vecc are non ...

If the vectors `veca, vecb, vecc` are non -coplanar and `l,m,n` are distinct scalars such that
`[(lveca+mvecb+nvecc, lvecb+mvecc+nveca,lvecc+mveca+nvecb)]=0` then

A

`x+y+z=0`

B

`xy+yz+zx=0`

C

`x^(3)+y^(3)+z^(3)=0`

D

`x^(2)+y^(2)+z^(2)=0`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • PRODUCT OF VECTORS

    ARIHANT MATHS ENGLISH|Exercise JEE Type Solved Examples: Passage Based Type Questions|3 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|12 Videos

  • PROBABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|54 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

Similar Questions

Explore conceptually related problems

If veca, vecb, vecc are non coplanar non null vectors such that [(veca, vecb, vecc)]=2 then {[(vecaxxvecb, vecbxxvecc, veccxxveca)]}^(2)=

If veca, vecb, vecc are non coplanar vectors and lamda is a real number, then [(lamda(veca+vecb), lamda^(2)vecb, lamdavecc)]=[(veca, vecb+vecc,vecb)] for

If veca, vecb,vecc are three non-coplanar vectors such that veca xx vecb=vecc,vecb xx vecc=veca,vecc xx veca=vecb , then the value of |veca|+|vecb|+|vecc| is

Statement 1: Any vector in space can be uniquely written as the linear combination of three non-coplanar vectors. Stetement 2: If veca, vecb, vecc are three non-coplanar vectors and vecr is any vector in space then [(veca,vecb, vecc)]vecc+[(vecb, vecc, vecr)]veca+[(vecc, veca, vecr)]vecb=[(veca, vecb, vecc)]vecr

If veca, vecb, vecc are non coplanar vectors and vecp, vecq, vecr are reciprocal vectors, then (lveca+mvecb+nvecc).(lvecp+mvecq+nvecr) is equal to

If the three vectors veca,vecb,vecc are non coplanar express each of vecbxxvecc, veccxxveca, vecaxxvecb in terms of veca,vecb,vecc .

If veca , vecb , vecc are non-coplanar vectors and lambda is a real number then [ lambda(veca+vecb) lambda^2vecb lambdavecc ] = [ veca vecb+vecc vecb ] for:

If veca, vecb, vecc are non-null non coplanar vectors, then [(veca-2vecb+vecc, vecb-2vecc+veca, vecc-2veca+vecb)]=

i. If veca, vecb and vecc are non-coplanar vectors, prove that vectors 3veca-7vecb-4vecc, 3veca-2vecb+vecc and veca+vecb+2vecc are coplanar.

If the vectors veca, vecb, and vecc are coplanar show that |(veca,vecb,vecc),(veca.veca, veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc)|=0

ARIHANT MATHS ENGLISH-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If the vectors veca, vecb, vecc are non -coplanar and l,m,n are distin...

    Text Solution

    |

  2. Let O be the origin and let PQR be an arbitrary triangle. The point S ...

    Text Solution

    |

  3. Let O be the origin and vec(OX) , vec(OY) , vec(OZ) be three unit vec...

    Text Solution

    |

  4. Let O be the origin, and O X , O Y , O Z be three unit vectors ...

    Text Solution

    |

  5. Let a, b and c be three unit vectors such that atimes(btimesc)=(sqrt(3...

    Text Solution

    |

  6. Let vec a , vec b and vec c be three non-zero vectors such that no ...

    Text Solution

    |

  7. If vec a , vec ba n d vec c are unit vectors satisfying | vec a- v...

    Text Solution

    |

  8. The vector(s) which is/are coplanar with vectors hat i+ hat j+2 hat...

    Text Solution

    |

  9. Let vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec ...

    Text Solution

    |

  10. Two adjacent sides of a parallelogram A B C D are given by vec A B=...

    Text Solution

    |

  11. Let P,Q R and S be the points on the plane with position vectors -2hat...

    Text Solution

    |

  12. If aa n db are vectors in space given by vec a=( hat i-2 hat j)/(sq...

    Text Solution

    |

  13. If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb)*(...

    Text Solution

    |

  14. The edges of a parallelopiped are of unit length and are parallel to ...

    Text Solution

    |

  15. Let two non-collinear unit vectors veca and vecb form an acute angle. ...

    Text Solution

    |

  16. Let the vectors PQ,OR,RS,ST,TU and UP represent the sides of a regular...

    Text Solution

    |

  17. The number of distinct real values of lambda , for which the vectors...

    Text Solution

    |

  18. Let veca,vecb,vecc be unit vectors such that veca+vecb+vecc=vec0. Whic...

    Text Solution

    |

  19. Let vec A be a vector parallel to the line of intersection of plan...

    Text Solution

    |

  20. Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec...

    Text Solution

    |

  21. The unit vector which is orthogonal to the vector 3hati+2hatj+6hatk an...

    Text Solution

    |