Home
Class 12
MATHS
The four lines drawing from the vertices...

The four lines drawing from the vertices of any tetrahedron to the centroid to the centroid of the opposite faces meet in a point whose distance from each vertex is 'k' times the distance from each vertex to the opposite face, where k is

A

`(1)/(3)`

B

`(1)/(2)`

C

`(3)/(4)`

D

`(5)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
(c)
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|28 Videos
  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|12 Videos
  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 4|7 Videos
  • THEORY OF EQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos
  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

Prove that the lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent.

Find the equation of the set of all points whose distances from (0,4)a r e2/3 of their distances from the line y=9.

Find the equation of the set of all points whose distances from (0,4) are 2/3 of their distances from the line y=9.

If K is the length of any edge of a regular tetrahedron, then the distance of any vertex from the opposite face is

Find the distance from the origin to each of the point: (4, -1, 2)

Find the distance from the origin to each of the point: (2,2,3)

Find the distance from the origin to each of the point: (0, 4,-4)

Find the equation to the locus of the point, the square of whose distance from origin is 4 times its y-coordinate.

Find the locus of a point which is such that, the three normals through it cut the axis in points whose distance from the vertex are in A.P.

The equation of the locus of a point which moves so that its distance from the point (ak, 0) is k times its distance from the point ((a)/(k),0) (k ne 1) is

ARIHANT MATHS ENGLISH-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. Show that x(1) hati+y(1) hatj+ z1hatk, x2hati+y2hatj+z2hatk and x3hati...

    Text Solution

    |

  2. The position vectors of points of intersection of three planes rcdotn1...

    Text Solution

    |

  3. A pentagon is formed by cutting a triangular corner from a rectangular...

    Text Solution

    |

  4. In a three-dimensional coordinate system, P ,Q ,a n dR are images o...

    Text Solution

    |

  5. A plane 2x+3y+5z=1 has a point P which is at minimum distance from lin...

    Text Solution

    |

  6. The locus of point which moves in such a way that its distance from th...

    Text Solution

    |

  7. A cube C={(x, y, z)|o le x, y, zle1} is cut by a sharp knife along the...

    Text Solution

    |

  8. A ray of light is sent through the point P(1,2,3) and is reflected on ...

    Text Solution

    |

  9. Find dy/dx if 2x-3sinx=2y

    Text Solution

    |

  10. The shortest distance between any two opposite edges of the tetrahedro...

    Text Solution

    |

  11. The angle between the pair of planes represented by equation 2x^(2)-2y...

    Text Solution

    |

  12. Let (p, q, r) be a point on the plane 2x+2y+z=6, then the least value ...

    Text Solution

    |

  13. The four lines drawing from the vertices of any tetrahedron to the cen...

    Text Solution

    |

  14. The shorteast distance from (1, 1, 1) to the line of intersection of t...

    Text Solution

    |

  15. The shortest distance between the two lines L1:x=k1, y=k2 and L2: x=k3...

    Text Solution

    |

  16. A=[{:(l(1),m(1),n(1)),(l(2),m(2),n(2)),(l(3),m(3),n(3)):}] and B=[{:(p...

    Text Solution

    |

  17. ABCD is a tetrahedron such that each of the triangleABC, triangleABD a...

    Text Solution

    |

  18. In a regular tetrahedron, if the distance between the mid points of op...

    Text Solution

    |

  19. A variable plane makes intercepts on X, Y and Z-axes and it makes a t...

    Text Solution

    |

  20. If P, Q, R, S are four coplanar points on the sides AB, BC, CD, DA of ...

    Text Solution

    |