Home
Class 12
MATHS
A variable plane at constant distance p ...

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

`a/x+b/y+c/z=1`

B

`ax+by+cz=1`

C

`a/x+b/y+c/z=-1`

D

`ax+by+cz=-1`

Text Solution

Verified by Experts

The correct Answer is:
A
NA
Promotional Banner

Topper's Solved these Questions

  • PLANE AND STRAIGHT LINE IN SPACE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|33 Videos

  • MISCELLANEOUS EQUATIONS AND INEQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|55 Videos

Similar Questions

Explore conceptually related problems

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 at a constant distance p from the origin meets the coordinate axes in points A,B and C respectively.Through these points , planes are drawn parallel to the coordinate planes, show that locus of the point of intersection is 1/x^2+1/y^2+1/z^2=1/p^2

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 passes through a fixed point (alpha,beta,gamma) and meets the axes at A ,B ,a n dCdot show that the locus of the point of intersection of the planes through A ,Ba n dC parallel to the coordinate planes is alphax^(-1)+betay^(-1)+gammaz^(-1)=1.

A variable plane passes through a fixed point (a,b,c) and meets the axes at A ,B ,a n dCdot The locus of the point commom to the planes through A ,Ba n dC parallel to the coordinate planes is

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 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) .

Find the distances of the point P(2, 3, 2) from the coordinate planes.

OBJECTIVE RD SHARMA ENGLISH-PLANE AND STRAIGHT LINE IN SPACE -Chapter Test
  1. The distance of the point having position vector -hat(i) + 2hat(j) + 6...

    Text Solution

    |

  2. The position vector of the point in which the line joining the points ...

    Text Solution

    |

  3. The two lines vecr=veca+veclamda(vecbxxvecc) and vecr=vecb+mu(veccxxve...

    Text Solution

    |

  4. Lines vecr = veca(1) + lambda vecb and vecr = veca(2) + svecb will lie...

    Text Solution

    |

  5. Equation of a line passing through (-1,2,-3) and perpendicular to the ...

    Text Solution

    |

  6. Find the Vector and Cartesian equation of line passing through (1, -2,...

    Text Solution

    |

  7. The distance between the planes given by vecr.(hati+2hatj-2hatk)+5=0...

    Text Solution

    |

  8. Find shortest distance between the line vecr = (5hati + 7hatj + 3ha...

    Text Solution

    |

  9. Find the shortest distance between the lines vecr=(hatii+2hatj+hatk)+l...

    Text Solution

    |

  10. Find the equation of the plane through the points (2,2,1) and (9,3,6) ...

    Text Solution

    |

  11. The equation of the plane containing the line vecr = hati + hatj + lam...

    Text Solution

    |

  12. Find ten equation of the plane passing through the point (0,7,-7) and ...

    Text Solution

    |

  13. Equation of the plane passing through the point (1,1,1) and perpendicu...

    Text Solution

    |

  14. A variable plane at constant distance p form the origin meets the coor...

    Text Solution

    |

  15. The equation of the line of intersection of the planes x+2y+z=3 and 6x...

    Text Solution

    |

  16. Find the Cartesian form the equation of the plane vec r=(s-2t) hat i...

    Text Solution

    |

  17. If the planes vecr.(2hati-lamda hatj+3hatk)=0 and vecr.(lamda hati+5ha...

    Text Solution

    |

  18. The equation of the plane perpendicular to the line (x-1)/1=(y-2)/(-1)...

    Text Solution

    |

  19. Find the equation of a plane which passes through the point (3, 2, ...

    Text Solution

    |

  20. Determine the point in XY-plane which is equidistant from thee poin...

    Text Solution

    |