Home
Class 12
MATHS
A line with positive direction cosines p...

A line with positive direction cosines passes through the point `P(2, -1, 2)` and makes equal angles with the coordinate axes. The line meets the plane `2x+y+z= 9` at point `Q`. Find the length of the line segment `PQ`.

A

1

B

`sqrt2`

C

`sqrt3`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    VMC MODULES ENGLISH|Exercise JEE MAIN (ARCHIVE)|87 Videos
  • STRAIGHT LINES

    VMC MODULES ENGLISH|Exercise JEE Advanced Archive (State true or false: Q. 42)|1 Videos
  • TRIGONOMETRIC IDENTITIES AND EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|11 Videos

Similar Questions

Explore conceptually related problems

A line with positive direction cosines passes through the point P(2, – 1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals

A line with positive direction cosines passes through the point P(2, – 1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals

Find the direction cosines of the line passing through two points

Find the direction cosines of a line which makes equal angles with the coordinate axes.

Find the direction cosines of the line passing through the two points (-1, 2, 3) and (2, -3, 5).

Find the direction cosines of the line passing through the two points ( 2, 4, 5) and (1, 2, 3) .

A straight line passes through the points P(-1, 4) and Q(5,-2). It intersects the co-ordinate axes at points A and B. M is the midpoint of the segment AB. Find : The equation of the line.

Find the equation of the lines through the point (3, 2) which make an angle of 45 with the line x-2y=3 .

Find the equation of the lines through the point (3, 2) which make an angle of 45^@ with the line x-2y=3 .

The direction cosines of the line passing through P(2,3,-1) and the origin are

VMC MODULES ENGLISH-THREE DIMENSIONAL GEOMETRY -JEE ADVANCED (ARCHIVE)
  1. Let P be the image of the point (3, 1, 7) with respect to the plane x...

    Text Solution

    |

  2. The equation of the plane passing through the point (1,1,1) and perpen...

    Text Solution

    |

  3. A line with positive direction cosines passes through the point P(2, -...

    Text Solution

    |

  4. Let P(3,2,6) be a point in space and Q be a point on line vec r=( hat...

    Text Solution

    |

  5. A plane which is perpendicular to two planes 2x-2y+z=0 and x-y+2z = 4 ...

    Text Solution

    |

  6. about to only mathematics

    Text Solution

    |

  7. If the straight lines (x-1)/(2)=(y+1)/(k)=(z)/(2) and (z+1)/(5)=(y+1)/...

    Text Solution

    |

  8. The equation of the plane containing the line 2x-5y""+""z""=""3;""x...

    Text Solution

    |

  9. The disatance of the point (1, 0, 2) from the point of intersection of...

    Text Solution

    |

  10. Perpendicular are drawn from points on the line (x+2)/(2)=(y+1)/(-1)=...

    Text Solution

    |

  11. The equation of a plane passing through the line of intersection of th...

    Text Solution

    |

  12. about to only mathematics

    Text Solution

    |

  13. If the distance of the point P(1,-2,1) from the plane x+2y-2z=alpha,...

    Text Solution

    |

  14. Equation of the plane containing the straight line (x)/(2)= (y)/(3)= (...

    Text Solution

    |

  15. Consider three planes P(1):x-y+z=1, P(2):x+y-z=-1 and P(3):x-3y+3z=2...

    Text Solution

    |

  16. Consider the planes 3x-6y-2z=15 and 2x+y-2z=5. Statement 1:The parame...

    Text Solution

    |

  17. From a point P(lambda, lambda, lambda), perpendicular PQ and PR are dr...

    Text Solution

    |

  18. Two lines L(1) : x=5, (y)/(3-alpha)=(z)/(-2) and L(2) : x=alpha, (y)/(...

    Text Solution

    |

  19. A line l passing through the origin is perpendicular to the lines l(...

    Text Solution

    |

  20. In R(3) , consider the planes P(1):y=0and P(2) : x+z=1. Let P(3) ...

    Text Solution

    |