Home
Class 12
MATHS
Find the vector equation of the plane pa...

Find the vector equation of the plane passing through the intersection of the planes `x-2y+z=1a n d2x+y+z=8` and parallel to the line with direction ratios proportional to `1,2,1.` Find also the perpendicular distance of `(1,1,1)` from this plane.

Text Solution

Verified by Experts

The correct Answer is:
`12/sqrt(194)`
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT SECTION - A|90 Videos

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT SECTION - B|47 Videos

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE ENGLISH|Exercise Illustration|4 Videos

  • STRAIGHT LINES

    AAKASH INSTITUTE ENGLISH|Exercise SECTION-J (AAKASH CHALLENGERS QUESTIONS)|5 Videos

  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Section - J (Akash Challengers Question)|16 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the plane passing through the intersection of the planes 4x-y+z=10\ a n d\ x+y-z=4 and parallel to the line with direction ratios proportional to 2, 1, 1.

The equation of the plane through the intersection of the planes x+y+z=1 and 2x+3y-z+4 = 0 and parallel to x-axis is

The equation of the plane through the intersection of the planes x+y+z=1 and 2x+3y-z+4 = 0 and parallel to x-axis is

Find the equation of the plane passing through the line of intersection of the planes 4x-5y-4z=1 and 2x+y+2z=8 and the point (2,1,3).

Find the equation of the plane passing through the intersection of the planes: x+y+z+1=0 and 2x-3y +5z-2=0 and the point (-1, 2,1)

Find the equation of plane through the line of intersection of the planes 3x – 4y + 5z = 10, 2x +2y-3z=4 and parallel to the line x=2y=3z

Find the equation of the plane passing through the intersection of the planes 2x-3y+z-4=0a n dx-y+z+1=0 and perpendicular to the plane x+2y-3z+6=0.

Find the equations of the line passing through the point (3,0,1) parallel to the planes x+2y=0 and 3y-z=0 .

Find the equations of the line passing through the point (3,0,1) parallel to the planes x+2y=0 and 3y-z=0 .

Find the vector equation of the line passing through the point (1,-1,2) and perpendicular to the plane 4x-2y-5z-2=0.

AAKASH INSTITUTE ENGLISH-THREE DIMENSIONAL GEOMETRY -TRY YOURSELF
  1. Find the equation of the plane passing through the points (1,-1,2)a n ...

    Text Solution

    |

  2. Find the equation of the plane through the points A(3, 2, 0), B(1, 3, ...

    Text Solution

    |

  3. Find equation of the plane through (2, 1, 4), (1, -1, 2) and (4, -1, 1...

    Text Solution

    |

  4. Find the equation of the plane containing the points P(2, 3, -1), Q(6,...

    Text Solution

    |

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

    Text Solution

    |

  6. A variable plane which remains at q constant distance 3p from the orig...

    Text Solution

    |

  7. Find the vector equation of a plane containing line of intersection of...

    Text Solution

    |

  8. Find the equation of the plane through the line of intersection of the...

    Text Solution

    |

  9. Find an equation for the plane through P(0)=(1, 0, 1) and passing thro...

    Text Solution

    |

  10. Find the equation of the plane containing the line of intersection of ...

    Text Solution

    |

  11. Show that lines (x-2)/5=(y+1)/1=(z-2)/-6 and (x+3)/-8=(y-2)/-1=(z-8)/7...

    Text Solution

    |

  12. Find x such that the four points A\ (3,\ 2,\ 1), B(4, x ,\ 5), C\ (4,...

    Text Solution

    |

  13. Find the angle between the two planes 2x + y-2z = 5and 3x- 6y-2z = 7...

    Text Solution

    |

  14. Find the angle between the planes 2x - y + 3z = 6 and x + y +2z =7.

    Text Solution

    |

  15. Find the angle between the line (x-1)/3=(y+1)/2=(z-1)/4 and plane 2x +...

    Text Solution

    |

  16. Find the angle between the line vecr=hati+2hatj-hatk+lamda(hati-hatj+h...

    Text Solution

    |

  17. Find the perpendicular distance from the point P(2, 3, -4) to the plan...

    Text Solution

    |

  18. Find the vector equation of the plane passing through the intersection...

    Text Solution

    |

  19. Find the distance of the point (-2, 3, -5) from the line (x+2)/1=(y-3)...

    Text Solution

    |

  20. Find the point on the line (x+2)/3=(y+1\ )/2=(z-3\ )/2 at a distanc...

    Text Solution

    |