Home
Class 12
MATHS
If from a point P(a ,b ,c) perpendicular...

If from a point `P(a ,b ,c)` perpendiculars `P Aa n dP B` are drawn to `Y Za n dZ X-p l a n e s` find the vectors equation of the plane `O A Bdot`

Text Solution

Verified by Experts

The coordinates of A are `(0,b,0)` and `(a,0,c)`
So,
`|[x-0,y-0,z-0],[0-0,b-0,c-0],[z-0,0-0,c-0]|=0`
`=>bcx+acy-abz=0 `
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

In fig. 28.7 if the coordinates of point P a r e (a , b , c) then Write the coordinates of points A, B, C, D, E and F. Write the coordinates of the feet of the perpendiculars from the point P to the coordinate axes. Write the coordinates of the feet of the perpendicular from the point P on the coordinate planes X Y , Y Z a n d Z Xdot Find the perpendicular distances of point P from X Y , Y Z a n d Z X- planes. Find the perpendicular distances of the point P fro the coordinate axes. Find the coordinates of the reflection of P are (a , b , c) . Therefore O A=a , O B=b n d O C=cdot

The foot of the perpendicular drawn from the origin to a plane is (1,2,-3). Find the equation of the plane.or If O is the origin and the coordinates of P is (1,2,-3), then find the equation of the plane passing through P and perpendicular to OP.

The foot of the perpendicular drawn from the origin O to a plane is N(12,-4,-3). Find the equation of the plane in cartesian form and vector form.

O A and O B are fixed straight lines, P is any point and P M and P N are the perpendiculars from P on O Aa n dO B , respectively. Find the locus of P if the quadrilateral O M P N is of constant area.

RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. Find the vector equation of the plane passing through the points A(2,2...

    Text Solution

    |

  2. Find the equation of the plane passing through the point (1,2,1) and p...

    Text Solution

    |

  3. If from a point P(a ,b ,c) perpendiculars P Aa n dP B are drawn to Y Z...

    Text Solution

    |

  4. Find the vector equation of the plane passing through the points havin...

    Text Solution

    |

  5. Find the equation of the plane through the points P(1,\ 1,\ 0),\ Q(1,\...

    Text Solution

    |

  6. Find the equation of the plane passing through the following points: (...

    Text Solution

    |

  7. Find the equation of the plane passing through the following points: (...

    Text Solution

    |

  8. Find the equation of the plane passing through the following points: (...

    Text Solution

    |

  9. Find the equation of the plane passing through the following points: (...

    Text Solution

    |

  10. Find the equation of the plane passing through the following points: (...

    Text Solution

    |

  11. Show that the following points are coplanar: (0,\ -1,\ 0),\ (2,\ 1,\ -...

    Text Solution

    |

  12. Show that the following points are coplanar: (0,\ 4,\ 3),\ (-1,\ -5,\ ...

    Text Solution

    |

  13. Show that the point (0, -1, -1), (4 5, 1), (3, 9, 4) and (-4, 4, 4) ar...

    Text Solution

    |

  14. Reduce the equation of the plane 2x+3y-z=6 to intercept form and find ...

    Text Solution

    |

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

    Text Solution

    |

  16. Reduce the equations of the following planes in intercept form and fin...

    Text Solution

    |

  17. Reduce the equation of the plane 2x+3y-4=12 to intercept form and find...

    Text Solution

    |

  18. Reduce the equations of the following planes in intercept form and fin...

    Text Solution

    |

  19. Find the equation of the plane passing through the point (2, 4, 6) and...

    Text Solution

    |

  20. Find the equation in Cartesian form of the plane passing through the ...

    Text Solution

    |