Home
Class 12
MATHS
A variable plane which remains at a cons...

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A,B,C. show that the locus of the centroid of the triangle ABC is `x^-2+y^-2+z^-2=p^-2`.

Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    PRADEEP PUBLICATION|Exercise EXERCISE|373 Videos

  • RELATIONS AND FUNCTIONS

    PRADEEP PUBLICATION|Exercise EXERCISE|401 Videos

  • VECTORS

    PRADEEP PUBLICATION|Exercise EXERCISE|438 Videos

Similar Questions

Explore conceptually related problems

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A,B,C. Show that locus of the O centroid of the triangle ABC is (1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(p^(2)) .

A variable plane which remains at a constant distance p from the origin cuts the coordinate axes in A, B, C. The locus of the centroid of the tetrahedron OABC is x^(2)y^(2)+y^(2)z^(2)+z^(2)x^(2)=(k)/(p^(2))x^(2)y^(2)z^(2), then root(5)(2k) is

A variable plane which is at a constant distance 3p from the origin meets the axes in points A, B and C respectively. Show that the locus of the centroid of Delta ABC is 1/x^2+1/y^2+1/z^2=1/(p^2)

A variable plane which is at a constant distance 6 p from the origin meets the axes in points A, B and C respectively. Show that the locus of the centroid of Delta ABC is 1/x^2+1/y^2+1/z^2=1/(4p^2)

A variable plane is at a distance k from the origin and meets the coordinates axes is A,B,C. Then the locus of the centroid of DeltaABC is

A variable plane which is at a constant 6 p from the origin meets the axes in A,B and C respectively. Show that the locus of the centroid of the triangle ABC is (1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(4p^(2))

A variable plane which remains at a constant distance p from the origin cuts the co-ordinate axes at A, B, C. Through A,B,C planes are drawn parallel to the co-ordinate planes. Show that locus of the point of intersection is : x^(-2)+y^(-2)+z^(-2)=p^-2

A variable plane is at a constant distance 4p from the origin and cuts axes in A, B, C respectively. Show that the centroid of the tetrahedron OABC lies on : 1/x^2+1/y^2+1/z^2=1/p^2

If the plane x/2+y/3+z/4=1 cuts the coordinate axes in A, B,C, then the area of triangle ABC is

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. A variable plane which remains at a constant distance 3p from the orig...

    Text Solution

    |

  2. Find the points on z-axis which are at a distance of sqrt21 from the p...

    Text Solution

    |

  3. Find k so that the distance between the points (7, 1, - 3) and (4,5, k...

    Text Solution

    |

  4. Find the point on x-axis which is equidistant from the point (1,3,2) a...

    Text Solution

    |

  5. Find the point which is equidistant from the points (a,0,0),(0,b,0),(0...

    Text Solution

    |

  6. Show that the points (2,4,3),(4,1,9) and (10,-1,6) are the vertices of...

    Text Solution

    |

  7. Find the locus of a point which is equidistant from the points (3,2,1...

    Text Solution

    |

  8. Find the point in the XY-plane which is equidistant from the points (2...

    Text Solution

    |

  9. Prove that the point A (0,0,0),B(2,0,0),C(1,sqrt3,0) and D(1,1/sqrt3, ...

    Text Solution

    |

  10. Find the coordinates of the point which divides the join of the points...

    Text Solution

    |

  11. Find the points on the line segment PQ situated at 2/3 of the distan...

    Text Solution

    |

  12. Find the points on the line segment PQ situated at 2/3 of the distan...

    Text Solution

    |

  13. If A and B are two points whose position vectors are 3hati+2hatj-2hatk...

    Text Solution

    |

  14. If A and B are two points whose position vectors are 3hati+2hatj-2hatk...

    Text Solution

    |

  15. Find the coordinates of the point which is three fifth of the way (3,4...

    Text Solution

    |

  16. Find the ratio in which the line segment joining : (1,2,3) and (-3,4,-...

    Text Solution

    |

  17. If A and B are the points (-3,4,-8) and (5,-6,4) respectively, find th...

    Text Solution

    |

  18. Using section formula, prove that the three points (-2,3,5),(1,2,3) an...

    Text Solution

    |

  19. Show that the points : (4, 7, 8), (2, 3, 4), (- 1, - 2, 1), (1, 2, 5) ...

    Text Solution

    |

  20. Using vectors, show that the medians of a triangle are concurrent.

    Text Solution

    |

  21. Prove that the points A(5,0,2), B(2,-6,0),C(4,-9,6) and D(7,-3,8), tak...

    Text Solution

    |