Home
Class 12
MATHS
Show that the line joining any vertex of...

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.

Promotional Banner

Topper's Solved these Questions

  • VECTORS

    MODERN PUBLICATION|Exercise Exercise|500 Videos

  • UNIT TEST-4

    MODERN PUBLICATION|Exercise EXERCISE|13 Videos

Similar Questions

Explore conceptually related problems

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

Show that the line segments joining the mid-points of opposite sides of a quadrilateral bisect each other.

Show that the line joining the mid points of two sides of a triangle is parallel to the third side.

Show that the diagonals of a parallelogram divide it into four triangles of equal area.

A quadrilateral is a parallelogram, if its one pair of opposite sides are equal and parallel.

Show that the perpendicular drawn from the point (4, 1) on the line segment joining (6, 5) and (2,-1) divides it internally in the ratio 8 : 5.

A median is a line segment that joins vertex and its perpendicular to the opposite side.

MODERN PUBLICATION-VECTORS-Exercise
  1. G is the centroid of a triangle ABC, show that : vec(GA)+vec(GB)+vec(G...

    Text Solution

    |

  2. Let veca,vecb,vecc,vecd be the position vectors of the four distinct p...

    Text Solution

    |

  3. Show that the line joining any vertex of a parallelogram to the mid-po...

    Text Solution

    |

  4. Prove that the figure formed by joining the mid-points of the pairs of...

    Text Solution

    |

  5. Show that if P,A,B are any three points, then lambda vec(PA)+mu vec(PB...

    Text Solution

    |

  6. Obtain the dot product of the vectors : veca=veci-hatj+hatk and vecb=v...

    Text Solution

    |

  7. Write the magnitude of a vector veca in terms of dot product.

    Text Solution

    |

  8. If veca=7hati+hatj-4hatk and vecb=2hati+6hatj+3hatk find the projectio...

    Text Solution

    |

  9. Let veca=2hati+3hatj+2hatk and vceb=hati+2hatj+hatk. Find the projecti...

    Text Solution

    |

  10. Find the projection of the vector hati-hatj on the vector hati+hatj.

    Text Solution

    |

  11. Find veca.vecb If veca=3hati-hatj+2hatk and vecb=2hati+3hatj+3hatk

    Text Solution

    |

  12. Find veca.vecb If veca=2hati-hatj+hatk and vecb=2hatj-hatk.

    Text Solution

    |

  13. Evaluate the product (3 hata-5hatb) cdot(2hata+7hatb)

    Text Solution

    |

  14. If veca is a unit vector and (vecx - veca) cdot (vecx + veca) = 8, th...

    Text Solution

    |

  15. If veca is a unit vcetor and (vecx-veca)*(vecx+veca)=80, then find |ve...

    Text Solution

    |

  16. If vecp is a unit vcetor and (vecx-vecp)*(vecx+vecp)=80, then find |ve...

    Text Solution

    |

  17. Find |vecx|, if for a unit vector veca, (vecx - veca)cdot(vecx+veca)...

    Text Solution

    |

  18. Find the angle between the vectors : hati-hatj and hatj-hatk.

    Text Solution

    |

  19. Find the angle between the vectors : hati+hatj+hatk and hati+hatj-hatk...

    Text Solution

    |

  20. Find the angle between the vectors veca=hati-2hatj+3hatk and vecb=3hat...

    Text Solution

    |