Home
Class 12
MATHS
The position vectors of three vertices A...

The position vectors of three vertices A,B,C of a tetrahedron OABC with respect to its vertex O are `hati,6hatj,hatk`, then its volume (in cu units) is

A

3

B

`1/3`

C

`1/6`

D

`6`

Text Solution

Verified by Experts

The correct Answer is:
D
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 the position vectors of the vertices of a triangle be 2hati+4hatj-hatk,4hati+5hatj+hatk and 3 hati+6hatj-3hatk , then the triangle is

If the verticles of a tetrahedron have the position vectors vec0, hati+hatj, 2hatj-hatk and hati+hatk then the volume of the tetrahedron is

If the position vectors of the vertices A,B and C of a triangleABC are respectively 4hati + 7hatj + 8hatk, 2hati + 4hatk and 2hati + 5 hatj + 7hatk ,then the positions vector of the point, where the bisector of angleA meets BC is:

If the position vectors of the vertices A,B and C of a DeltaABC are 7hatj+10k,-hati+6hatj+6hatk and -4hati+9hatj+6hatk , respectively, the triangle is

The position vectors of the vertices A, B and C of triangle are hati+hatj, hatj+hatk and hati+hatk , respectively. Find the unit vectors hatr lying in the plane of ABC and perpendicular to IA , where I is the incentre of the triangle.

ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. The position vectors of three vertices A,B,C of a tetrahedron OABC wit...

    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

    |