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|Exercise Exercise For Session 1|13 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise For Session 2|19 Videos

  • PROBABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|55 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|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 three non-coplanar mutually perpendicular unit vectors, then [(veca, vecb, vecc)] is

If veca, vecb, vecc are non-coplanar unit vectors such that vecaxx(vecbxxvecc)=(vecb+vecc)/(sqrt(2)) then the angle between veca and vecb is

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 and vecc are unit coplanar vectors, then the scalar triple product [(2veca-vecb, 2vecb-vecc, 2vecc-veca)]=

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 veca, vecb and vecc are unit coplanar vectors , then the scalar triple porduct [2 veca -vecb" " 2vecb - vecc " "2vecc-veca] is

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

ARIHANT MATHS-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 OX, OY, OZ be three unit vectors in the direct...

    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 a, b and c are unit vectors satisfying |a-b|^(2)+|b-c|^(2)+|c-a|^(2...

    Text Solution

    |

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

    Text Solution

    |

  9. Let vec a =hat i+hat j+hat k,vec b=hat i -hat j+hat k and vec c =hat ...

    Text Solution

    |

  10. Two adjacent sides of a parallelogram ABCD are given by vec(AB)=2hati+...

    Text Solution

    |

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

    Text Solution

    |

  12. If a and b are vectors in space given by a=(hat(i)-2hat(j))/(sqrt(5)) ...

    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. Lelt two non collinear unit vectors hata and hatb form and acute angle...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. Let A be vector parallel to line of intersection of planes P1 and P2. ...

    Text Solution

    |

  20. Let a=hat(i)+2hat(j)+hat(k), b=hat(i)-hat(j)+hat(k), c=hat(i)+hat(j)-h...

    Text Solution

    |

  21. If vec a , vec b and vec c are three non-zero, non coplanar vecto...

    Text Solution

    |