Home
Class 12
MATHS
Show that the points (1,-2,-3),(2,-3,-1)...

Show that the points (1,-2,-3),(2,-3,-1) and (3,-1,-2) are the vertices of an equilateral triangle

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • CARTESIAN AND POLAR COORDINATE SYSTEM

    MAHAVEER PUBLICATION|Exercise QUESTION BANK|26 Videos

  • CO-ORDINATE GEOMETRY OF TWO DIMENSIONS (CONIC SECTION)

    MAHAVEER PUBLICATION|Exercise QUESTION BANK|110 Videos

Similar Questions

Explore conceptually related problems

show that the points A(1,-1,-5), B(3,1,3) and C(9,1,-3) are the vertices of an equilateral triangle.

Prove that the points (5,3,2),(3,2,5) and (2,5,3) are the vertices of an equilateral triangle.

Show that the points A(1,2),B(1,6), C(1 + 2sqrt(3),4) are the vertices of an equilateral 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), B(-1, -1) and C(-sqrt3, sqrt3) are the vertices of an equilateral triangle each of whose sides is 2sqrt2 units.

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.

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

Prove that the points A(2, 4), B(2, 6) and C(2 + sqrt(3) , 5) are the vertices of an equilateral triangle.

Show that the points (-3, -3), (3, 3) and (-3sqrt(3), 3sqrt(3)) are the vertices of an equilateral triangle.

MAHAVEER PUBLICATION-CO-ORDINATE GEOMETRY OF THREE DIMENSIONS-QUESTION BANK
  1. Find the distances between the following pair of points. (-4,-2,3) and...

    Text Solution

    |

  2. If the distance between the points (x,2,0) and (1,3,1) be sqrt6 , find...

    Text Solution

    |

  3. Show that the points (1,-2,-3),(2,-3,-1) and (3,-1,-2) are the vertice...

    Text Solution

    |

  4. Show that the triangle with vertices (6,10,10),(1,0,-5) and (6,-10,0)...

    Text Solution

    |

  5. Find the locus of the point which is equidistant from the points (1,-2...

    Text Solution

    |

  6. The distance of a point from the x-axis is twice its distance from the...

    Text Solution

    |

  7. A point moves in such a way that its distance from the X-axis is twice...

    Text Solution

    |

  8. Find the co-ordinates of the point which divides the join of (5,8,-3) ...

    Text Solution

    |

  9. In what ratio does the origin divides the line segment joining the poi...

    Text Solution

    |

  10. Find the co-ordinates of the centroid of the triangle whose vertices a...

    Text Solution

    |

  11. Find the point of intersection of the medians of the triangle whose ve...

    Text Solution

    |

  12. Find the lengths of the medians of the triangle whose vertices are A(2...

    Text Solution

    |

  13. Can there be any line which makes angles 30^@,45^@ and 60^@ with the c...

    Text Solution

    |

  14. If a line makes angles 60^@ and 135^@ respectively with x and y axes f...

    Text Solution

    |

  15. If a line makes angles alpha, beta and gamma with the co-ordinate axes...

    Text Solution

    |

  16. Find the direction cosines of the line whose direction ratio are 2,-4,...

    Text Solution

    |

  17. Find the direction cosines of the line whose direction ratio are sqrt3...

    Text Solution

    |

  18. Find the direction cosines of the line whose direction ratio are a-b,b...

    Text Solution

    |

  19. If a line make angle 30^@ and 60^@ with the x and y axes, what angles ...

    Text Solution

    |

  20. Find the direction ratios and direction cosines of the lines joining t...

    Text Solution

    |