Home
Class 12
MATHS
Prove that the lines joining the midpoin...

Prove that the lines joining the midpoints of consecutive sides of a quadrilateral form a parallelogram using vector method.

Promotional Banner

Topper's Solved these Questions

  • TEST PAPER 1

    MODERN PUBLICATION|Exercise PROBLEM|75 Videos

  • TEST PAPER 2

    MODERN PUBLICATION|Exercise PROBLEM|74 Videos

Similar Questions

Explore conceptually related problems

Prove by vector method that the lines joining the mid points of consecutive sides of a quadrilateral is a parallelogram.

Prove by vector method that the line segment joining the mid points of two sides of a triangle is parallel to the third and half of it.

Prove analytically : The line segment joining the midpoints of two sides of a triangle is parallel to the third and half of its length.

Prove by vector method that the diagonals of a quadrilateral bisect each other iff is a parallelogram.

Prove by vector method that the diagonals of a parallelogram bisect each other.

Prove that magnitude of cross product of two vectors is equal to the area of the parallelogram with those two sides as vectors.

Prove that the sum of the vectors directed from the vertices to the mid points of opposite sides of a triangle is zero

Prove by vector method that in a parallelogram, the line joining a vertex to the midpoint of an oppositeside trisects the other diagonal.

Prove that the line joining (1,2,3),(2,1,-1) intersects the line joining (-1,3,1) and (3,1,5) .

MODERN PUBLICATION-TEST PAPER 10-EXERCISE
  1. Solve x + 2y = 3, 3x + y = 4 by matrix method.

    Text Solution

    |

  2. Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

    Text Solution

    |

  3. If A=[[alpha,0],[1,1]] and B=[[1,0],[5,1]], show that for no values of...

    Text Solution

    |

  4. Prove that |(1, a, a^3),(1, b, b^3),(1, c, c^3)|= (a-b)(b-c)(c-a)(a+b+...

    Text Solution

    |

  5. If x^7y^3=(x+y)^10, then find (d^2y)/(dx^2)

    Text Solution

    |

  6. If tangents are drawn from the origin to the curve y = sin x, then sho...

    Text Solution

    |

  7. Integrate the following int(3x+4)/(xsqrt(2x^2-5))dx

    Text Solution

    |

  8. Evaluate int(0)^(4)(x+e^(2x))dx, as limit of sum.

    Text Solution

    |

  9. Solve : (dy)/(dx)= sin(x+y)+cos(x+y)

    Text Solution

    |

  10. Solve the following differential equations (1-x^2)(dy)/(dx)+2xy= x s...

    Text Solution

    |

  11. If vec a, vec b, vec c are mutually perpendicular vectors of equal mag...

    Text Solution

    |

  12. Prove that the lines joining the midpoints of consecutive sides of a q...

    Text Solution

    |

  13. int0^1(x^5(4-x^2))/sqrt(1-x^2)dx

    Text Solution

    |

  14. find the point of intersection of the line through (1,3,-2) and (3,4,1...

    Text Solution

    |

  15. Prove that the lines frac[x+3][2]=frac[y+5][3]=frac[z-7][-3] and frac[...

    Text Solution

    |

  16. Let R be the relation on the set R of real numbers such that aRb iff a...

    Text Solution

    |

  17. Show that f : A to B, where A=R - {3}, B=R - {1} defined as f(x)=(x-2)...

    Text Solution

    |

  18. Find the particular solution of the differential equation dy/dx+y cot ...

    Text Solution

    |

  19. Prove that the curves y^(2)=4x and x^(2)=4y divide the area of the squ...

    Text Solution

    |

  20. A line with direction ratios lt2,1,2gt meets each of the lines x=y+a=z...

    Text Solution

    |