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. The length of the line segment PQ equals

A

1

B

`sqrt(2)`

C

`sqrt(3)`

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • PLANE IN SPACE

    MARVEL PUBLICATION|Exercise PREVIOUS YEAR MHT-CET EXAM QUESTIONS|3 Videos

  • PLANE IN SPACE

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP- CHAPTERS 6,7,8|16 Videos

  • PLANE IN SPACE

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP- CHAPTERS 6,7,22|1 Videos

  • PAIR OF STRAIGHT LINES

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|19 Videos

  • THREE DIMENSIONAL GEOMETRY

    MARVEL PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS|39 Videos

Similar Questions

Explore conceptually related problems

A line with positive direction cosines passes through the ont P(2,-1,2) and makes equal angles with the coordinate axes. The line meets the plane 2x+y+z=9 at Q. The length of the line segment PQ equals (A) 1 (B) sqrt(2) (C) sqrt(3) (D) 2

What is the equation of straight line passing through the point (4, 3) and making equal intercepts on the coordinate axes ?

If a line passes through the point P(1, 2) makes an angle of 45^(@) with the x axis and meets the line x + 2y - 7 = 0 in Q, then PQ equals

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

Equation of a line which passes through point A(2,3) and makes an angle of 45 with x axis.If this line meet the line x+y+1=0 at point P then distance AP is

A normal line with positive direction cosines to the plane P makes equal angles with the coordinate axis. The distance of the point A(1, 2, 3) from the line (x-1)/(1)=(y+2)/(1)=(z-3)/(2) measured parallel to the plane P is equal to

Equation of the straight line which passes through the point A(2,3) makes an angle 45 with x -axis.If this line meets the line x+y+1=0 at P. Then the distance of AP is

Equation of the straight line which passes through the point A(2,3) makes an angle 45widehat A with x -axis.If this line meets the line x+y+1=0 at P. Then the distance of AP is

MARVEL PUBLICATION-PLANE IN SPACE -PART B: MASTERING THE BEST ON LINE AND PLANE IN SPACE
  1. The projection of a vector on the three coordinate axes are 6, -3, 2, ...

    Text Solution

    |

  2. The plane barr = s(i+2j-4k) +t(3i+4j-4k) +(1-t)(2i-7j+3k) is paralle...

    Text Solution

    |

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

    Text Solution

    |

  4. The equation of the plane containing the straight line x/2=y/3=z/4 and...

    Text Solution

    |

  5. If a plane meets coordinate axes in points A,B,C such that the centroi...

    Text Solution

    |

  6. Find the equations of the bisectors of the angles between the plane...

    Text Solution

    |

  7. If the perpendicular distance of a point A, other than the origin from...

    Text Solution

    |

  8. Under what condition do the planes bx-ay=n,cy-bz=l,az-cx=m intersect ...

    Text Solution

    |

  9. If the two lines, whose d.C.s l,m,n are given by the equation al+bm+cn...

    Text Solution

    |

  10. The straight lines, whose direction cosines are l, m, n which are the ...

    Text Solution

    |

  11. The perpendicular distance of a corner of uni cube from a diagonal not...

    Text Solution

    |

  12. A line makes an angle alpha, beta, gamma, delta with the four diagonal...

    Text Solution

    |

  13. If the centroid of the tetrahedron O-ABC, where A-=(alpha,5,6), B-=(1,...

    Text Solution

    |

  14. The shortest distance between the lines x+a=2y=-12z and x=y+2a=6z-6a i...

    Text Solution

    |

  15. The direction Cosines of two lines at right angles are l(1),m(1),n(1)a...

    Text Solution

    |

  16. Two system of rectangular axes have the same origin. If a plane cuts t...

    Text Solution

    |

  17. If h, m1, n1 and l2, m2, n2 are D.C.s of the two lines inclined to eac...

    Text Solution

    |

  18. Let vectors bara, barb, barc and bard be such that (baraxxbarb)xx(ba...

    Text Solution

    |

  19. A non zero vector veca is parallel to the kine of intersection of the ...

    Text Solution

    |

  20. Value of k such that the line (x-4)/1 = (y-2)/1 =(z-k)/2 lies in th...

    Text Solution

    |