Home
Class 12
MATHS
In any triangle ABC, show that AB^(2)+...

In any triangle ABC, show that
`AB^(2)+AC^(2)=2(AD^(2)+BD^(2))`
where, D is the middle point of BC.

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

In any triangle ABC, prove that AB^2 + AC^2 = 2(AD^2 + BD^2) , where D is the midpoint of BC.

If D(-2, 3), E (4, -3) and F (4, 5) are the mid-points of the sides BC, CA and AB of the sides BC, CA and AB of triangle ABC, then find sqrt((|AG|^(2)+|BG|^(2)-|CG|^(2))) where, G is the centroid of Delta ABC .

In any triangle ABC, prove that cos A= frac{b^2+c^2-a^2}{2bc} .

In Fig. D is a point on side BC of triangleABC such that (BD)/(CD) = (AB)/(AC) . Prove that AD is the bisector of angleBAC .

In fig., D is a point on side BC of triangleABC such that (BD)/(DC)=(AB)/(AC) . Prove that, AD is bisector of angleBAC . .

A, B, C and D are four points in space. Using vector methods, prove that AC^(2)+BD^(2)+AC^(2)+BC^(2)geAB^(2)+CD^(2) what is the implication of the sign of equality.

In any triangle ABC, then by vectors, prove that : c^2=a^2+b^2-2ab cos C .

In Fig if AD bot BC , prove that AB^2 + CD^2 = BD^2 + AC^2 .

Prove that, in any triangle ABC, cos C=(a^2+b^2-c^2)/(2ab) .

In figure, AD is a median of a triangle ABC and AM bot BC. Prove that AC ^(2) + AB ^(2) = 2 AD ^(2) + (1)/(2) BC ^(2).

MODERN PUBLICATION-VECTORS-Exercise
  1. Use vectors to prove that in triangleABC : b=c cos A+a cos C.

    Text Solution

    |

  2. Using vector method prove that cos(A-B)=cosAcosB+sinAsinB

    Text Solution

    |

  3. In any triangle ABC, show that AB^(2)+AC^(2)=2(AD^(2)+BD^(2)) wher...

    Text Solution

    |

  4. Prove that any two edges in a regular tetrahedron are perpendicular.

    Text Solution

    |

  5. In each problem, find the work done by a force vecF acting on a partic...

    Text Solution

    |

  6. In each problem, find the work done by a force vecF acting on a partic...

    Text Solution

    |

  7. Find the work done by the force vecF=hati+2hatj+hatk acting on a parti...

    Text Solution

    |

  8. Find the work done in moving an object along the vector vecd=3hati+2ha...

    Text Solution

    |

  9. A particle acted by constant forces 4 hat i+ hat j-3 hat k and 3 hat...

    Text Solution

    |

  10. Constant forces 2hati-5hatj+6hatk and hati+2hatj-hatk act on a particl...

    Text Solution

    |

  11. Forces of magnitudes 5 and 3 units acting in the directions 6hati + ...

    Text Solution

    |

  12. Which is greater: 45 kg or 4500 g?

    Text Solution

    |

  13. Find vecaxxvecb, if : veca=-hati+3hatk and vecb=hati+3hatj-2hatk.

    Text Solution

    |

  14. Find vecaxxvecb, if : veca=hati-3hatj+4hatk and vecb=2hati+hatj+hatk.

    Text Solution

    |

  15. The value of : hati*(hatjxxhatk)+hatj*(hatkxxhati)+hatk*(hatjxxhati) i...

    Text Solution

    |

  16. The value of : hati*(hatjxxhatk)+hatj*(hatixxhatk)+hatk*(hatixxhatj) i...

    Text Solution

    |

  17. Find the value of 'p' is : (2hati+6hatj+27hatk)xx(hati+3hatj+phatk)=ve...

    Text Solution

    |

  18. If veca=hati-hatj+2hatk and vecb=2hati+hatj-hatk, find : (2veca-vecb)x...

    Text Solution

    |

  19. Find vecaxxvecb, if veca=2hati+hatj+3hatk and vecb=3hati+5hatj-2hatk

    Text Solution

    |

  20. If veca=4hati+3hatj+hatk and vecb=hati-2hatk, then find |2vecbxxveca|.

    Text Solution

    |