Home
Class 11
MATHS
Show that the points A(0,1,2),B(2,-1,3)a...

Show that the points `A(0,1,2),B(2,-1,3)a n dC(1,-3,1)` are vertices of an isosceles right-angled triangle.

Text Solution

Verified by Experts

Given,`A(0,1,2),B(2,-1,3),C(1,-3,1) so,AB`=`sqrt((2−0)^2+(−1−1)^2+(3−2)^2) ​=3`
BC=`sqrt((2−1)^2+(−1+3)^2+(3−1)^2) ​=3`
CA=`sqrt((1−0)^2+(−3−1)^2+(1−2)^2) ...
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    RD SHARMA|Exercise Solved Examples And Exercises|72 Videos
  • LIMITS

    RD SHARMA|Exercise All Questions|300 Videos

Similar Questions

Explore conceptually related problems

Show that the points (2,-1,3), (0,1,2) and (1,-3,1) are the vertices of an isosceles right angled triangle.

Show that the points A(2,-1,3),B(1,-3,1) and C(0,1,2) are the vertices of an isosceles right angled triangle.

Show that the points A(1,1,1) ,B(1,2,3) and C(2,-1,1) are vertices of an isosceles triangle

Show that the points A(7, 10), B(-2, 5) and C(3, -4) are the vertices of an isosceles right-angled triangle.

Show that the points (0,7,10),(-1,6,6) and (-4,9,6) are the vertices of an isosceles right angled triangle.

Show that the points (-4,-4,-1),(0,2,3) and (4,6,-3) are the vertices of an isosceles right angled triangle.

Show that the points A(-5, 6), B(3, 0) and C(9, 8) are the vertices of an isosceles right-angled triangle. Calculate its area.

Prove that the points (5, -2), (-4, 3) and (10, 7) are the vertices of an isosceles right-angled triangle.

Show that the points A(3, 0), B(6, 4) and C(-1, 3) are the vertices of an isosceles right triangle.

Using vector method, show that the points A(1,-1,0), B(4,-3,1) and C(2,-4,5) are the vertices of a right -angled triangle.

RD SHARMA-INTRODUCTIONS TO 3-D COORDINATE GEOMETRY-Solved Examples And Exercises
  1. Prove by using distance formula that the points A(1,2,3),B(-1,-1,-1)an...

    Text Solution

    |

  2. Determine the point in X Y-p l a n e whcih is equidistant from three p...

    Text Solution

    |

  3. Show that the points A(0,1,2),B(2,-1,3)a n dC(1,-3,1) are vertices of ...

    Text Solution

    |

  4. Find the coordinates of a point equidistant from th four points O(0,0,...

    Text Solution

    |

  5. Find the point on y-axis which is equidistant from the points (3,1,2)...

    Text Solution

    |

  6. Prove that the triangle formed by joining the three points whose co...

    Text Solution

    |

  7. The lines joining the vertices of a tetrahedron to the centroids of...

    Text Solution

    |

  8. Using the section formula, prove that the three pints A(-2,3,5),B(1...

    Text Solution

    |

  9. Find the coordinates of the points which trisect the line segment A...

    Text Solution

    |

  10. Find the ratio in which the join the A(2,1,5)a n dB(3,4,3) is divided ...

    Text Solution

    |

  11. In fig. 28.7 if the coordinates of point P\ a r e\ (a , b , c) then Wr...

    Text Solution

    |

  12. Planes r drawn parallel to the coordinate planes through the point P(x...

    Text Solution

    |

  13. Name the octants in which the following points lie: (5,2,3)

    Text Solution

    |

  14. Name the octants in which the following points lie: (-5,-4,7)

    Text Solution

    |

  15. Name the octants in which the following points lie: (-5,4,3)

    Text Solution

    |

  16. Name the octants in which the following points lie: (-5,-3,-2)

    Text Solution

    |

  17. Name the octants in which the following points lie: (4,-3,5)

    Text Solution

    |

  18. Name the octants in which the following points lie: (2,-5,-7)

    Text Solution

    |

  19. Name the octants in which the following points lie: (7,4,-3)

    Text Solution

    |

  20. Name the octants in which the following points lie: (-7,2,-5)

    Text Solution

    |