Home
Class 12
MATHS
Prove that if a plane has intercepts a,b...

Prove that if a plane has intercepts a,b,c and is at a distance of p units from the origin, then `1/a^2+1/b^2+1/c^2=1/p^2`.

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

Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin, then 1/a^2 + 1/b^2 + 1/c^2 = 1/p^2

Two systems of rectangular axes have the same origin. If a plane cuts them at distance a,b,c and a',b',c' respectively form the origin, prove that 1/a^2+1/b^2+1/c^2=1/(a'^2)+1/(b'^2)+1/(c'^2) .

The differential equation of all straight lines which are at a constant distance p from the origin, is (a) (y+xy_1)^(2)=p^(2) (1+y_(1)^2) (b) (y-xy_(1)^(2))=p^(2) (1+y_(1))^(2) ( c ) (y-xy_(1))^(2)=p^(2) (1+y_(1)^(2)) (d) None of these

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that 1/p^2=1/a^2+1/b^2 .

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that (1)/(p^(2)) = (1)/(a^(2)) +(1)/(b^(2)) .

If p_1, p_2, p_3 are the altitudes of a triangle from the vertices A, B, C and triangle , the area of the triangle, prove that : 1/p_1+1/p_2-1/p_3= (2ab)/((a+b+c)triangle) cos^2 frac (C)(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 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)

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Find the vector equation of the line passing through (1, 2, 3) and par...

    Text Solution

    |

  2. Find the vector equation of the line passing through the point (1,2,-4...

    Text Solution

    |

  3. Prove that if a plane has intercepts a,b,c and is at a distance of p u...

    Text Solution

    |

  4. Find the Distance between the two planes 2x+3y+4z=4 and 4x+6y+8z=12

    Text Solution

    |

  5. The planes 2x - y + 4z = 5 and 5x - 2.5y + 10z = 6 are :

    Text Solution

    |

  6. The x, co-ordinate of a point on the line joining the points Q (2, 2, ...

    Text Solution

    |

  7. Find the distance of the point (-1 , -5 , -10) from the point of inter...

    Text Solution

    |

  8. Find the equation of a plane which is at a distance 3sqrt3 units from ...

    Text Solution

    |

  9. Find the equation of the two lines through the origin which intersect ...

    Text Solution

    |

  10. The plane ax+by=0 is rotated through an angle alpha about its line of ...

    Text Solution

    |

  11. Show that the sequence t n defined by t n = 3 n + 1 is an AP.

    Text Solution

    |

  12. Prove that the lines, whose direction cosines are given by al+bm+cn=0,...

    Text Solution

    |

  13. Prove that the lines, whose direction cosines are given by al+bm+cn=0,...

    Text Solution

    |

  14. Using converse of Basic Proportionality theorem prove that the line jo...

    Text Solution

    |

  15. Verify that <(l1+l2+l3)/sqrt3,(m1+m2+m3)/sqrt3,(n1+n2+n3)/sqrt3> can b...

    Text Solution

    |

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

    Text Solution

    |

  17. The two lines x=ay+b, z=cy+d and x=a'y+b', z=c'y+d' are perpendicular ...

    Text Solution

    |

  18. Prove that the line joining the points vec(6a)-vec(4b)+vec(4c) and -ve...

    Text Solution

    |

  19. Find the vector equation of the line passing through (1, 2, 3) and par...

    Text Solution

    |

  20. Find the vector equation of the line passing through the point (1,2,-4...

    Text Solution

    |