Home
Class 12
MATHS
The line which contains all points (x, y...

The line which contains all points `(x, y, z)` which are of the form `(x, y, z)=(2, -2, 5)+lambda(1, -3, 2)` intersects the plane `2x-3y+4z=163` at P and intersects the YZ-plane at Q. If the distance PQ is `asqrt(b)`, where `a,binN and agt3`, then `(a+b)` is equalto

A

`23`

B

`95`

C

`27`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
(a)
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|28 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|14 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise For Session 4|7 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

The line which contains all points (x,y,z) which are of the frrom (x,y,z)=(2,-2,5)+lambda(1,-3,2) interseets the plane 2x-3y=4z=163 at and intersets the YZ plane Q.If the distance PQ is a sqrt(b) where a,b in N and a>3 then (a+b) equals

The point at which the line joining the points (2, -3, 1) and (3, -4, -5) intersects the plane 2x+y+z=7 is

Are the planes x+y-2z+4=0 and 3x+3y-6z+5=0 intersecting

If the line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the plane 2x+3y-z+13=0 at a point P and the plane 3x+y+4z=16 at a point Q, then PQ is equal to

Line (x-2)/(-2) = (y+1)/(-3) = (z-5)/1 intersects the plane 3x+4y+z = 3 in the point

If the line (x-2)/(3)=(y+1)/(2)=(z-1)/(2) intersects the plane 2x+3y-z+13=0 at a point P and plane 3x+y+4z=16 at a point Q then PQ is equal to

Point of intersection of the line (x-1)/2 = (y-2)/3 = (z+3)/4 and the plane 2x+4y -z=1 is

ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. The lines (x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and (x-1)/(k)=(y-4)/(2)=(z-5)...

    Text Solution

    |

  2. The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve xy=c^2, z...

    Text Solution

    |

  3. The line which contains all points (x, y, z) which are of the form (x,...

    Text Solution

    |

  4. If the three planes rcdotn1=p1, rcdotn2=p2 and rcdotn3=p3 have a commo...

    Text Solution

    |

  5. The equation of the plane which passes through the line of intersectio...

    Text Solution

    |

  6. A straight line is given by r=(1+t)i+3tj+(1-t)k, where tinR. If this l...

    Text Solution

    |

  7. The distance of the point (-1, -5, -10) from the point of intersection...

    Text Solution

    |

  8. P(vec p) and Q(vec q) are the position vectors of two fixed points and...

    Text Solution

    |

  9. The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a ...

    Text Solution

    |

  10. The orthogonal projection A' of the point A with position vector (1, 2...

    Text Solution

    |

  11. The equation of the line passing through (1, 1, 1) and perpendicular t...

    Text Solution

    |

  12. A variable plane at a distance of 1 unit from the origin cuts the axes...

    Text Solution

    |

  13. The angle between the lines AB and CD, where A(0, 0, 0), B(1, 1, 1), C...

    Text Solution

    |

  14. The shortest distance of a point (1, 2, -3) from a plane making interc...

    Text Solution

    |

  15. A tetrahedron has vertices O(0,0,0),A(1,2,1),B(2,1,3),a n dC(-1,1,2), ...

    Text Solution

    |

  16. The direction ratios of the line I1 passing through P(1, 3, 4) and per...

    Text Solution

    |

  17. Equation of the plane through three points A, B and C with position ve...

    Text Solution

    |

  18. OABC is a tetrahedron. The position vectors of A, B and C are I, i+j a...

    Text Solution

    |

  19. The plane x-y-z=4 is rotated through an angle 90^(@) about its line of...

    Text Solution

    |

  20. A(xy),(yz),A(zx) be the area of projections oif asn area a o the xy,yz...

    Text Solution

    |