Home
Class 12
MATHS
A variable plane passes through a fixed ...

A variable plane passes through a fixed point a,b,c and meet the co-ordinates axes in A,B,C. Show that the locus of the point common to the planes through A,B,C parallel to the co-ordinate planes is `a/x+b/y+c/z=1`

Promotional Banner

Topper's Solved these Questions

  • Three Dimensional Geometry

    MODERN PUBLICATION|Exercise EXERCISE|491 Videos
  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXAMPLE|13 Videos
  • UNIT TEST-4

    MODERN PUBLICATION|Exercise EXERCISE|13 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 plane passes through a fixed point (a, b, c) and direction ratios of the normal to the plane are (2, 3 , 4) find the equation of the plane

A plane meets the coordinate axes in A ,B ,C such that the centroid of triangle A B C is the point (p ,q ,r)dot Show that the equation of the plane is x/p+y/q+z/r=3.

Find the equation of the plane passing through origin and parallel to the plane x+3y-2z+7=0 .

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 .

Find the equation of the plane through the point (1,4,-2) and parallel to the plane 2x-y+3z+7=0 .

Find the perpendicular distances of the point P (a, b, c) from the co-ordinate axes.

Find the co-ordinates of the points A,B,C and D in the given figure.

Find the equation of plane passing through the point (1,4,-2) and parallel to the plane 2x-y+3z=0

Planes are drawn through the points (5, 0, 2) and (3, - 2, 5) parallel to the co-ordinates planes. Find the lengths of the edges of the rectangular parallelopiped so formed.

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. A variable plane is at a constant distance 4p from the origin and cuts...

    Text Solution

    |

  2. A variable plane which remains at a constant distance p from the origi...

    Text Solution

    |

  3. A variable plane passes through a fixed point a,b,c and meet the co-or...

    Text Solution

    |

  4. A variable plane moves so that the sum of reciprocals of its intercept...

    Text Solution

    |

  5. Show that the sum of the reciprocals of the intercepts on rectangular ...

    Text Solution

    |

  6. Find the equations of the bisector planes of the angle between the pla...

    Text Solution

    |

  7. In the following case, determine whether the given planes are parallel...

    Text Solution

    |

  8. In the following case, determine whether the given planes are parallel...

    Text Solution

    |

  9. In the following case, determine whether the given planes are parallel...

    Text Solution

    |

  10. ਪIn the following case, determine whether the given planes are paralle...

    Text Solution

    |

  11. In the following case, determine whether the given planes are parallel...

    Text Solution

    |

  12. What is the point of intersection of the line x=y=z with the plane x+2...

    Text Solution

    |

  13. Find the angle between the lines in which the planes: 3x-7y-5z=1, 5x-1...

    Text Solution

    |

  14. Show that the line , vecr=2hati-3hatj+5hatk+lambda(hati-hatj+2hatk) li...

    Text Solution

    |

  15. Show that the line , vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in t...

    Text Solution

    |

  16. Find the vector equation of the line passing through the point (3,1,2)...

    Text Solution

    |

  17. Find the point where the line (x+1)/2=(y+2)/3=(z+3)/4 meets the plane ...

    Text Solution

    |

  18. Find the angle between the line : (2hati+3hatj+4hatk)+lambda(2hati+3ha...

    Text Solution

    |

  19. Find the angle between the line joing (3,-4,-2) and(12, 2, 0) and the ...

    Text Solution

    |

  20. Find the angle between the line : (x+1)/2=y/3=(z-3)/6 and the plane 10...

    Text Solution

    |