Home
Class 11
MATHS
The lines joining the vertices of a tetr...

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

Text Solution

Verified by Experts

It is true that The lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent.
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    RD SHARMA|Exercise Solved Examples And Exercises|72 Videos

  • LIMITS

    RD SHARMA|Exercise All Questions|300 Videos

Similar Questions

Explore conceptually related problems

The fout 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

Show that the segments joining vertices to the centroid of opposite faces of a tetrahedron are concurren Hence find the position vector of the point of concurrence.

Prove that the perpendicular let fall from the vertices of a triangle to the opposite sides are concurrent.

Medians the line segments joining the vertices to the mid-points of the opposite side of a triangle are known as its medians.

Prove that the volume of the tetrahedron and that formed by the centroids of the faces are in the ratio of 27:1.

Find the ratio of the volume of tetrahedron with that of the tetrahedron formed by the centroids of its faces. Given Volume of tetrahedron =1/3 times area of base triangle times height of vertex.

Show that the line joining any vertex of a parallelogram to the mid - point of an opposite side divides the opposite diagonal in the ratio 2 : 1.

Line segments joining the vertices to the mid- points of the opposite sides to a triangle are known as medians (b) altitudes (c) heights (d) angle bisectors

RD SHARMA-INTRODUCTIONS TO 3-D COORDINATE GEOMETRY-Solved Examples And Exercises
  1. Find the point on y-axis which is equidistant from the points (3,1,2)...

    Text Solution

    |

  2. Prove that the triangle formed by joining the three points whose co...

    Text Solution

    |

  3. The lines joining the vertices of a tetrahedron to the centroids of...

    Text Solution

    |

  4. Using the section formula, prove that the three pints A(-2,3,5),B(1...

    Text Solution

    |

  5. Find the coordinates of the points which trisect the line segment A...

    Text Solution

    |

  6. Find the ratio in which the join the A(2,1,5)a n dB(3,4,3) is divided ...

    Text Solution

    |

  7. In fig. 28.7 if the coordinates of point P\ a r e\ (a , b , c) then Wr...

    Text Solution

    |

  8. Planes r drawn parallel to the coordinate planes through the point P(x...

    Text Solution

    |

  9. Name the octants in which the following points lie: (5,2,3)

    Text Solution

    |

  10. Name the octants in which the following points lie: (-5,-4,7)

    Text Solution

    |

  11. Name the octants in which the following points lie: (-5,4,3)

    Text Solution

    |

  12. Name the octants in which the following points lie: (-5,-3,-2)

    Text Solution

    |

  13. Name the octants in which the following points lie: (4,-3,5)

    Text Solution

    |

  14. Name the octants in which the following points lie: (2,-5,-7)

    Text Solution

    |

  15. Name the octants in which the following points lie: (7,4,-3)

    Text Solution

    |

  16. Name the octants in which the following points lie: (-7,2,-5)

    Text Solution

    |

  17. Find the image of: (-2,3,4) in the yz-planes.

    Text Solution

    |

  18. Find the image of: 5,2,-7) in the xy-planes.

    Text Solution

    |

  19. Find the image of: (-4,0,0) in the xy-planes.

    Text Solution

    |

  20. Find the image of: (-5,4,-3) in the xz-planes.

    Text Solution

    |