Home
Class 12
MATHS
Find the vector and cartesian equation o...

Find the vector and cartesian equation of the plane passing through the point (1,2,3) and perpendicular to the line with direction ratio `lt2,3,-4gt`.

Text Solution

Verified by Experts

The correct Answer is:
`[vec(r)-(hat(i)+2hat(j)+3hat(k))]*(2hat(i)+3hat(j)-4hat(k))=0;2x+3y-4z=-4`
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT MOST IMPORTANT QUESTIONS FOR PRACTICE (SECTION VII) Short Answer Type Questions |13 Videos

  • THREE DIMENSIONAL GEOMETRY

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT MOST IMPORTANT QUESTIONS FOR PRACTICE (SECTION VIII) Long Answer Type Questions |24 Videos

  • THREE DIMENSIONAL GEOMETRY

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT MOST IMPORTANT QUESTIONS FOR PRACTICE (SECTION V) Short Answer Type Questions |10 Videos

  • RELATIONS AND FUNCTIONS

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE |43 Videos

  • VECTOR ALGEBRA

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE (MCQ)|46 Videos

Similar Questions

Explore conceptually related problems

Find the vector and cartesian equations of the plane which passes through the point (5,2,-4) and perpendicular to the line with direction ratios ,

Find the vector and cartesian equations of the plane which passes through the point (5, 2, – 4) and perpendicular to the line with direction ratios 2, 3, – 1.

Find the vector and cartesion equation of the line through the point (1,2,3) and (2,-1,4).

Find the vector equations of the line passing through the point (1,-1,2) and perpendicular to the plane 2x-y+3z-5=0.

Find the vector and cartesian equations of the line that passes through : the points (1,2,3) and (2,-1,4).

Find the equations of the line passing through the point (1,-1,2) and perpendicular to the plane 2x-y+3z=5.

Find the vector equation for the line passing through the points (–1, 0, 2) and (3, 4, 6).

The equation of straight line passing through the point (2, 3) and perpendicular to the line 4x -3y = 10 is:

Find the equations of the line passing through the point (-4,3,1) perpendicular to the plane x+2y-z=0 .

Find the vector equation of the plane passing through the points (2,5,-3),(-2,-3,5) and (5,3,-3).

BETTER CHOICE PUBLICATION-THREE DIMENSIONAL GEOMETRY -ASSIGNMENT MOST IMPORTANT QUESTIONS FOR PRACTICE (SECTION VI) Short Answer Type Questions
  1. The length of the perpendicular drawn from the origin to 2x-3y+6z+21=0

    Text Solution

    |

  2. Find the intercepts cut off by the plane x+2y-2z=9 with the axes.

    Text Solution

    |

  3. Find the vector and cartesian equation of the plane passing through th...

    Text Solution

    |

  4. Find the equation of the plane passing through origin and parallel to ...

    Text Solution

    |

  5. Find the equation of plane passing through the point (1,4,-2) and para...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Find the angle between the following planes vec(r)*(hat(i)+hat(j)-2h...

    Text Solution

    |

  9. Find the angle between the following planes vec(r)*(3hat(i)-4hat(j)+...

    Text Solution

    |

  10. Find the angle between the following pair of lines

    Text Solution

    |

  11. Find the equation of plane passing through the intersection of the pla...

    Text Solution

    |

  12. Find the vector equation of the plane through the intersection of the ...

    Text Solution

    |

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

    Text Solution

    |

  14. Find the equation of the plane passing through the line of intersectio...

    Text Solution

    |

  15. Find the equation of the through to the line of intersection of the pl...

    Text Solution

    |

  16. Find the equations of the planes passing through the following points ...

    Text Solution

    |

  17. Find the equations of the planes passing through the following points ...

    Text Solution

    |

  18. Find the equations of the planes passing through the following points ...

    Text Solution

    |

  19. Find the equations of the planes passing through the following points ...

    Text Solution

    |

  20. Show that the points (-6,3,2),(3,-2,4),(5,7,3) and (-13,17,-1) are cop...

    Text Solution

    |