Home
Class 12
MATHS
Prove that the sum of the vectors direct...

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

Promotional Banner

Topper's Solved these Questions

  • MATRICES DETERMINANTS PROBABILITY

    USHA PUBLICATION|Exercise EXERCISE|59 Videos

  • PRACTICE PAPER

    USHA PUBLICATION|Exercise PRACTICE PAPER|95 Videos

Similar Questions

Explore conceptually related problems

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 that the sum of the vectors represented by the sides of a closed polygon taken in order is a zero vector.

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

Prove that the sum of all the vectors drawn from the centre of a regular octagon to its vertices is the null vector.

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 mid-point of the hypotentise of a right angles triangle is equidistance from the vertices.

In a triangle one of the vertices is at (2,5) and the centroid of the triangle is at (-1,1). Find the coordinates of the midpoint of the side opposite to the given angular point.

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

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Evaluate the following integrals int(3sinx+28cosx)/(5sinx+6cosx)dx

    Text Solution

    |

  2. Find the equation of the plane passing through the line (x-8)/3=(y+19)...

    Text Solution

    |

  3. Prove that the sum of the vectors directed from the vertices to the mi...

    Text Solution

    |

  4. If A (1,0,-1), B (-2,4,-2) and C(1,5,10) be the vertices of a triangle...

    Text Solution

    |

  5. Find the image of the point (3,-2,1) in the plane x-y+3z=2.

    Text Solution

    |

  6. Prove the following by vector method. The diagonals of a rhombus are a...

    Text Solution

    |

  7. Prove that intdx/((x-1)^2(x+2))=1/9ln abs((x+2)/(x-1))-1/(3(x-1))+c

    Text Solution

    |

  8. int0^pi((xtanx)/(secx+tanx))dx

    Text Solution

    |

  9. Solve: (1+x^2)dy/dx+2xy-x^3=0

    Text Solution

    |

  10. Find (dy)/(dx) if x=(3at)/(1+t^3), y=(3at^2)/(1+t^3) at t=1/2

    Text Solution

    |

  11. If x cos alpha + y sin alpha = p is a tangent to the curve (x/a)^(n/...

    Text Solution

    |

  12. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

    Text Solution

    |

  13. If A=[(0,1,0),(-1,0,2),(0,0,1)], then show that A^3-A^2+I3=[(2,-1,0),(...

    Text Solution

    |

  14. If "cos"^(-1)(x/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)...

    Text Solution

    |

  15. Solve the following LPP graphically: Maximize: Z=4x1+3x2 subject to x1...

    Text Solution

    |

  16. Prove by vector method that in any triangle ABC, a/sinA=b/sinB=c/sinC.

    Text Solution

    |

  17. A line makes angles alpha, beta, gamma, delta with the four main diago...

    Text Solution

    |

  18. If veca, vecb, vecc are mutually perpendicular vectors of equal magnit...

    Text Solution

    |

  19. The equation of a plane passing through (1, 1, 2) and parallel to x + ...

    Text Solution

    |

  20. What is the value of int0^100[tan^(-1)x]dx ?

    Text Solution

    |