Home
Class 11
MATHS
In a triangle ABC, if D and E are mid po...

In a triangle ABC, if D and E are mid points of sides AB and AC respectively. Show that `vecBE+ vecDC=(3)/(2)vecBC`.

Text Solution

Verified by Experts

The correct Answer is:
`(3)/(2)vecBC`
Promotional Banner

Topper's Solved these Questions

  • Vector Algebra -I

    PREMIERS PUBLISHERS|Exercise Solution to Exercise (8.1)|13 Videos

  • Vector Algebra -I

    PREMIERS PUBLISHERS|Exercise Solution to Exercise(8.2)|27 Videos

  • TWO DIMENSIONAL ANALYTICAL GEOMETRY

    PREMIERS PUBLISHERS|Exercise PROBLEM FOR PRACTICE (CHOOSE THE CORRECT OPTION)|28 Videos

Similar Questions

Explore conceptually related problems

If D and E, are the midpoints of the sides AB and AC of a triangle ABC, prove that vec(BE) +vec(DC)=(3)/(2)vec(BC).

Let A, B, and C be the vertices of a triangle. Let D, E, and F be the midpoints of the sides BC, CA, and AB respectively. Show that vec(AD)+vec(BE)+vec(CF)=vec(0) .

In DeltaABC, D, E and F are the midpoints of sides AB, BC and CA respectively. Show that DeltaABC is divided into four congruent triangles, when the three midpoints are joined to each other. (ΔDEF is called medial triangle)

In the adjacent figure, we have AC = XD, C and D are mid points of AB and XY respectively. Show that AB = XY.

In the figure, ABC is a triangle in which AB= AC. Points D and E are points on the side AB and AC respectively such that AD=AE. Show that points B, C, E and D lie on a same circle.

A,B, and C are vertice of DeltaABC,D,E and F are mid point of side AB,BC and AC respectively. If the coordinates of A, D and F are (-3,5),(5,1) and (-5,-1) respectively. Find the coordinates of B,C and E.

In Delta ABC , D and E are points on the sides AB and AC respectively. For each of the following cases show that DE||BC (i) AB=12 cm , AD=8 cm, AE=12 cm and AC=18 cm. (ii) AB=5.6 cm, AD=1.4 cm, AC=7.2 cm and AE=1.8 cm.

PREMIERS PUBLISHERS-Vector Algebra -I-Choose Correct Option
  1. In a triangle ABC, if D and E are mid points of sides AB and AC respec...

    Text Solution

    |

  2. If vec a,vecb,vecc are sides of triangle taken in order then avec+bvec...

    Text Solution

    |

  3. Let O be the origin . Let A and B be two points whose position vectors...

    Text Solution

    |

  4. Let vecr=xveci+yvecj+zveck be the position vector of any point and let...

    Text Solution

    |

  5. If m(veci+vecj+veck) is a unit vector then value of m is:

    Text Solution

    |

  6. A vector vecOP makes 60^(@) each with positive direction of x and y ax...

    Text Solution

    |

  7. If veca =veci-2vecj+veck,vecb=2veci-vecj+2veck, vecc=3veci+vecj-veck b...

    Text Solution

    |

  8. If O is the origin and A,B are the points (2,1,-3) and (1,1,1) respect...

    Text Solution

    |

  9. For any two vectors veca and vecb|veca X vecb|^(2)+|veca.vecb| is:

    Text Solution

    |

  10. If veca,vecb and vecc are three unit vectors satisfying veca-vecb-sqrt...

    Text Solution

    |

  11. Show that vecaxx(vecb+vecc)+vecbxx(vecc+veca)+veccxx(veca+vecb)=vec0.

    Text Solution

    |

  12. Two vertices of a triangle hence position vetors 2veci+4vecj-5veck and...

    Text Solution

    |

  13. If 2veca+6vecb and 3veca+mvecb are parallel then the vector of m is:

    Text Solution

    |

  14. Match the following

    Text Solution

    |

  15. Find the incorrect statement

    Text Solution

    |

  16. Find the incorrect statement

    Text Solution

    |

  17. Find the correct statement

    Text Solution

    |

  18. Find the correct statement: Given vec OA =veca, vecOB=vecb and vecOP =...

    Text Solution

    |

  19. The vectors veca-vecb,vecb-vecc,vecc-veca are

    Text Solution

    |

  20. Find the odd man out.

    Text Solution

    |

  21. Find which in suitable for the blank space given below:|veca.vecb|…….....

    Text Solution

    |