Home
Class 12
MATHS
Find the equation of a plane passing th...

Find the equation of a plane passing through the parallel lines `(x-3)/(1) = (y+2)/(-4) = z/5`
and `(z-4)/(1) = (y-3)/(-4) = (z-2)/(5)` are coplanar. Also find the equation of plane in which these lines lie.

Text Solution

AI Generated Solution

To find the equation of a plane passing through the parallel lines given by the equations: 1. \(\frac{x-3}{1} = \frac{y+2}{-4} = \frac{z}{5}\) 2. \(\frac{x-4}{1} = \frac{y-3}{-4} = \frac{z-2}{5}\) we will follow these steps: ### Step 1: Identify Points and Direction Ratios ...
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 11 A|22 Videos
  • THREE-DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 11 B|30 Videos
  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos
  • VECTORS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the plane passing through the parallel lines (x-3)/(3) = (y+4)/(2) = (z-1)/(1) and (x+1)/(3)= (y-2)/(2) = z/1 .

Find the equation of the plane passing through the line (x-1)/5=(y+2)/6=(z-3)/4 and point (4,3,7)dot

The line through of the plane passing through the lines (x-4)/(1)=(y-3)/(1)=(z-2)/(2) and (x-3)/(1)=(y-2)/(-4)=(z)/(5) is

Find the equation of a line passing through (1,-1,0) and parallel to the line (x-2)/3=(2y+1)/2=(5-z)/1

Show that the lines (x-3)/2=(y+1)/(-3)=(z+2)/1 and (x-7)/(-3)=y/1=(z+7)/2 are coplanar. Also find the equation of the plane containing them.

Show that the lines (x+3)/(-3)=y-1/1=(z-5)/5;(x+1)/(-1)=(y-2)/2=(z-5)/5 are coplanar. Also find the equation of the plane containing the lines.

Show that the lines (x+1)/(-3)=(y-3)/2=(z+2)/1\ a n d\ x/1=(y-7)/(-3)=(z+7)/2 are coplanar. Also, find the equation of the plane containing them.

Find the equation of the plane passing through (1,2,0) which contains the line (x+3)/3=(y-1)/4=(z-2)/(-2)

Find the equation of a plane which passes through the point (3, 2, 0) and contains the line (x-3)/1=(y-6)/5=(z-4)/4

Find the equation of the plane passing through (1,2,3) and perpendicular to the straight line (x)/(-2) =(y)/(4) =(z)/(3) .

NAGEEN PRAKASHAN ENGLISH-THREE-DIMENSIONAL GEOMETRY -Miscellaneous Exercise
  1. Find the equation of a plane passing through the parallel lines (x-3)...

    Text Solution

    |

  2. Show that the line joining the origin to the point (2,1,1) is perpe...

    Text Solution

    |

  3. If l(1), m(1), n(1) and l(2),m(2),n(2) are the direction cosines of tw...

    Text Solution

    |

  4. Find the angle between the lines whose direction ratios are a, b, c a...

    Text Solution

    |

  5. Find the equation of a line parallel to x-axis and passing through ...

    Text Solution

    |

  6. If the coordinates of the points A ,B ,C ,D are (1,2,3),(4,5,7),(-4,3,...

    Text Solution

    |

  7. If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/2and (x-1)/(3k)=(y-1)/1=(z-6...

    Text Solution

    |

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

    Text Solution

    |

  9. Write the vector equation of the plane, passing through the point (a ,...

    Text Solution

    |

  10. Find the shortest distance between lines vecr = 6hati+2hatj+2hatk+lam...

    Text Solution

    |

  11. Find the coordinate of the point where the line through (5, 1, 6) and ...

    Text Solution

    |

  12. Find the coordinates of the point where the line through (5, 1, 6) ...

    Text Solution

    |

  13. Find the coordinates of the point where the line through (3, -4, -5...

    Text Solution

    |

  14. Find the equation of the plane passing through the point (-1, 3, 2)...

    Text Solution

    |

  15. If the points (1," "1," "p)" "a n d" "(" "3," "0," "1) be equidistant ...

    Text Solution

    |

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

    Text Solution

    |

  17. If O be the origin and the coordinates of P be(1," "2," "" "3) , th...

    Text Solution

    |

  18. Find the equation of the plane which contains the line of intersection...

    Text Solution

    |

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

    Text Solution

    |

  20. Find the vector equation o the line passing through (1,2,3) and parall...

    Text Solution

    |

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

    Text Solution

    |