Home
Class 12
MATHS
A plane meets the coordinate axes at A ,...

A plane meets the coordinate axes at `A ,Ba n dC` respectively such that the centroid of triangle `A B C` is `(1,-2,3)dot` Find the equation of the plane.

Text Solution

Verified by Experts

Since they meet at A,B,C so,
`A/3=B/3=C/3=(1,-2,3)`
So,
`A=3 B=-6 and C=9`
Thus,
equation are,
`x/(3)=y/(-6)=z/9=1`
Promotional Banner

Topper's Solved these Questions

  • TANGENTS AND NORMALS

    RD SHARMA|Exercise Solved Examples And Exercises|244 Videos
  • TRIGONOMETRIC IDENTITIES

    RD SHARMA|Exercise EXAMPLE|1 Videos

Similar Questions

Explore conceptually related problems

If a plane meets the coordinates axes at A Band C,in such a way that the centroid of Delta ABC is at the point (1,2,3), the equation of the plane is

If a plane meets the coordinate axes at A,B and C such that the centroid of the triangle is (1,2,4) then the equation of the plane is

A plane P meets the coordinate axes at A B and C respectively . The centroid of Delta ABC is give to be (1,1,2) . Then the equation of the line through this centroid and perpendicular to the plane P is ,

If a plane meets the coordinate axes in A,B and C such that the centroid of triangleABC is (1,2,4), then the equation of the plane is

A plane cuts the co-ordinate axes at A, B and C respectively. If the centroid of DeltaABC is (2,-3,4) , find the equation of the plane.

A plane meets the coordinate axes at A ,\ B ,\ C such that the centroid of "Delta A B C is the point (a ,\ b ,\ c) . If the equation of the plane is x/a+y/b+z/c=k ,\ t h e n\ k= 1 b. 2 c. 3 d. none of these

A plane meets the coordinates axis in A, B, C such that the centroid of the triangle ABC is the point (alpha, beta, gamma) . Find the equation of plane in intercept form.

RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. Find the distance between the line vec r=(- hat i+3 hat k)+lambda( ha...

    Text Solution

    |

  2. Find the image of the point having position vector hati + 3hatj + 4hat...

    Text Solution

    |

  3. A plane meets the coordinate axes at A ,Ba n dC respectively such that...

    Text Solution

    |

  4. Find the equation of a plane which meets the axes in A ,Ba n dC , give...

    Text Solution

    |

  5. Show that the four points (0,-1,-1),(-4,4,4),(4,5,1)a n d(3,9,4) are ...

    Text Solution

    |

  6. If from a point P(a ,b ,c) prpendiculars P Aa n dP B are drawn to y za...

    Text Solution

    |

  7. Find the equation of the plane through the points A(2,2,-1),B(3,4,2)a ...

    Text Solution

    |

  8. A variable plane moves in such a way that the sum of the reciprocals o...

    Text Solution

    |

  9. A plane meets the coordinate axes in A ,B ,C such that eh centroid of ...

    Text Solution

    |

  10. Write the equation of the plane whose intercepts on the coordinate axe...

    Text Solution

    |

  11. Show that the four point (0,-1,-1),(4,5,1),(3,9,4)a n d(-4,4,4) are co...

    Text Solution

    |

  12. Find the image of the point (1,3,4) in the plane 2x-y+z+3=0.

    Text Solution

    |

  13. Find the image of the point with position vector 3 hat i+ hat j+2 hat ...

    Text Solution

    |

  14. Find the length and the foot of perpendicular from the point (1,3//...

    Text Solution

    |

  15. Find the distance between the point with position vector hat i-5 hat ...

    Text Solution

    |

  16. Find the equation of the plane through the intersection of the planes ...

    Text Solution

    |

  17. Show that the plane whose vector equation is vec rdot( hat i+2 hat j-...

    Text Solution

    |

  18. Prove that the lines (x+1)/3=(y+3)/5=(z+5)/7a n d(x-2)/1=(y-4)/4=(z-6)...

    Text Solution

    |

  19. Show that the lines vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat ...

    Text Solution

    |

  20. Find the distance of the point P(-1,-5,-10) from the point of intersec...

    Text Solution

    |