Home
Class 12
MATHS
(Apollonius theorem): If D is the midpoi...

(Apollonius theorem): If D is the midpoint of the side BC of a triangle ABC, then show by vector method that
` |vec(AB)|^(2) + |vec(AC)|^(2) = 2(|vec(AD)|^(2)+ |vec(BD)|^(2)). `

Text Solution

Verified by Experts

The correct Answer is:
` (|vec(AD)|^(2)+|vec(BD)|^(2)) `
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF VECTOR ALGEBRA

    FULL MARKS|Exercise EXERCISE-6.1|14 Videos
  • APPLICATIONS OF VECTOR ALGEBRA

    FULL MARKS|Exercise EXERCISE-6.2|10 Videos
  • APPLICATIONS OF MATRICES AND DETERMINANTS

    FULL MARKS|Exercise ADDITIONAL QUESTIONS SOLVED|56 Videos
  • COMPLEX NUMBERS

    FULL MARKS|Exercise EXERCISE - 2.9|25 Videos

Similar Questions

Explore conceptually related problems

If D is the midpoint of the side BC of a triangle ABC, prove that vec(AB)+vec(AC)=2vec(AD)

If D is the midpoint of the side AB of a triagle ABC prove that vec(BC)+vec(AC)=-2vec(CD)

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).

The value of |vec(a)+vec(b)|^(2)+|vec(a)-vec(b)|^(2) is

If vec a and vec b are orthogonal vectors, prove that (vec a + vec b)^(2) = (vec a - vec b)^(2) .

If ABCDE is a pentagon then prove that vec(AB)+vec(AE)+vec(BC)+vec(DC)+vec(ED)+vec(AC)=3vec(AC)

Show that (vec a - vec b) xx (vec a + vec b) = 2 (vec a xx vec b)

If D,E and F are the mid-points of the sides BC, CA and AB respectively of a triangle ABC and lambda is scalar, such that vec(AD) + 2/3vec(BE)+1/3vec(CF)=lambdavec(AC) , then lambda is equal to

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) .

If ABCD is a quadrilateral and E and F are the midpoints of AC and BD respectively, then prove that vec(AB)+vec(AD)+vec(CB)+vec(CD)=4vec(EF) .

FULL MARKS-APPLICATIONS OF VECTOR ALGEBRA-Additional Questions Solved
  1. (Apollonius theorem): If D is the midpoint of the side BC of a triangl...

    Text Solution

    |

  2. The work done by the force vecF=ahati+hatj+hatk in moving the point...

    Text Solution

    |

  3. If the position vectors of three points A, B and Care respectively v...

    Text Solution

    |

  4. A force given by and 3veci+2vecj-4veck is applied at the point (1,-1...

    Text Solution

    |

  5. Show that the area of a parallelogram having diagonals 3veci+vecj-2v...

    Text Solution

    |

  6. If the edges  veca=-3veci+7vecj+5veck , vecb=-5veci+7vecj-3veck ,...

    Text Solution

    |

  7. If vecx.veca=0 , vecx.vecb=0 , vecx.vecc=0 and vecxnevec0 ...

    Text Solution

    |

  8. The volume of the parallelepiped whose edges are represented by -12 ha...

    Text Solution

    |

  9. Prove that |vecavecbvecc|=abc   if and only if veca , vecb , ...

    Text Solution

    |

  10. Show that the points (1, 3, 1), (1, 1,-1), (-1, 1, 1), (2,2, -1) are l...

    Text Solution

    |

  11. If veca=2veci+3vecj-5veck , vecb=-veci-vecj+2veck and vecc=4vec...

    Text Solution

    |

  12. If veca =3veci+2vecj-4veck , vecb =5veci-3vecj+6veck , vecc =5ve...

    Text Solution

    |

  13. If veca =2veci+3vecj-veck , vecb =2veci+5veck , vecc =vecj-3veck...

    Text Solution

    |

  14. Find the vector and cartesian equations of the straight line passing t...

    Text Solution

    |

  15. Find the vector and cartesian equations of the straight line passing t...

    Text Solution

    |

  16. Find the angle between the following lines vecr=3veci+2vecj-veck+t(v...

    Text Solution

    |

  17. Find the angle between the following lines (x-1)/(2)=(y+1)/(3)=(z-4)...

    Text Solution

    |

  18. Find the distance between the parallel lines vecr=(hati-hatj)+t(2hati-...

    Text Solution

    |

  19. Show that the lines vecr=(hati-hatj)+t(2hati+hatk) and vecr=(2hati-hat...

    Text Solution

    |

  20. Show that the lines (x-1)/(3)=(y-1)/(-1)=(z+1)/(0) and (x-4)/(2)=...

    Text Solution

    |

  21. find the shortest distance between the skew lines. vecr=(veci-vecj)+...

    Text Solution

    |