Home
Class 12
MATHS
If a variable plane forms a tetrahedron ...

If a variable plane forms a tetrahedron of constant volume `64k^3` with the co-ordinate planes, then the locus of the centroid of the tetrahedron is:

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise ARCHIVES INTEGER TYPE|1 Videos

Similar Questions

Explore conceptually related problems

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 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

If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A,B anc C, then the locus of the centroid of Delta ABC is :

A variable plane is at a constant distance p from the origin and meets the coordinate axes in A , B , C . Show that the locus of the centroid of the tetrahedron O A B C is x^(-2)+y^(-2)+z^(-2)=16p^(-2)

A variable plane is at a constant distance p from the origin and meets the coordinate axes in A , B , C . Show that the locus of the centroid of the tehrahedron O A B Ci sx^(-2)+y^(-2)+z^(-2)=16p^(-2)dot

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 triangle ABC is x^(-2) + y^(-2) + z^(-2) = p^(-2) .

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 triangle ABC is 1/x^2+1/y^2+1/z^2=1/p^2 .

A variable plane at constant distance p form the origin meets the coordinate axes at P,Q, and R. Find the locus of the point of intersection of planes drawn through P,Q, r and parallel to the coordinate planes.

A sphere of constant radius 2k passes through the origin and meets the axes in A ,B ,a n dCdot The locus of a centroid of the tetrahedron O A B C is a. x^2+y^2+z^2=4k^2 b. x^2+y^2+z^2=k^2 c. 2(x^2+y^2+z)^2=k^2 d. none of these

A sphere of constant radius 2k passes through the origin and meets the axes in A ,B ,a n dCdot The locus of a centroid of the tetrahedron O A B C is a. x^2+y^2+z^2=4k^2 b. x^2+y^2+z^2=k^2 c. 2(x^2+y^2+z)^2=k^2 d. none of these

CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions
  1. If the distance between the plane Ax-2y+z=d. and the plane containing ...

    Text Solution

    |

  2. Prove that the volume of tetrahedron bounded by the planes vec rdo...

    Text Solution

    |

  3. If a variable plane forms a tetrahedron of constant volume 64k^3 with ...

    Text Solution

    |

  4. O A ,O Ba n dO C ,w i t hO as the origin, are three mutually perpen...

    Text Solution

    |

  5. Prove that for all values of lambda and mu , the planes (2x)/a+y/b+(...

    Text Solution

    |

  6. If P is any point on the plane l x+m y+n z=pa n dQ is a point on the l...

    Text Solution

    |

  7. find the equation of the plane with intercepts 2,3 and 4 on the x, y a...

    Text Solution

    |

  8. A variable plane l x+m y+n z=p(w h e r el ,m ,n are direction cosines ...

    Text Solution

    |

  9. P is a point and P Ma n dP N are the perpendicular form Ptoz-xa n dx-y...

    Text Solution

    |

  10. Let a plane a x+b y+c z+1=0,w h e r ea ,b ,c are parameters, make an ...

    Text Solution

    |

  11. Let x-ysin alpha-zsin beta=0,xsin alpha+zsin gamma-y=0 and xsin beta+y...

    Text Solution

    |

  12. The position vectors of the four angular points of a tetrahedron OABC ...

    Text Solution

    |

  13. Find the distance of the point (-2,3,-4) from the line ("x"+2)/3=(2"...

    Text Solution

    |

  14. The plane 4x+7y+4z+81=0 is rotated through a right angle about its ...

    Text Solution

    |

  15. If (a, b, c) is a point on the plane 3x + 2y + z = 7, then find the ...

    Text Solution

    |

  16. Let the equation of the plane containing the line x-y - z -4=0=x+y+ 2z...

    Text Solution

    |

  17. Let a1, a2, a3.......... be in A.P. and h1,h2,h3.....,in H.P. If a1=2 ...

    Text Solution

    |

  18. If the angle between the plane x-3y+2z=1 and the line (x-1)/2=(y-1)/...

    Text Solution

    |

  19. The length of projection of the line segment joining the points (1,...

    Text Solution

    |

  20. Find the equation of a plane passing through (1, 1, 1) and parallel to...

    Text Solution

    |