Home
Class 12
MATHS
Consider a set of point R in which is a...

Consider a set of point R in which is at a distance of 2 units from the line `(x)/(1)= (y-1)/(-1)= (z+2)/(2)` between the planes `x-y+2z=3=0 and x-y+2z-2=0`. (a) The volume of the bounded figure by points R and the planes is `(10/3sqrt3)pi` cube units (b) The area of the curved surface formed by the set of points R is `(20/sqrt6)pi` sq. units The volume of the bounded figure by the set of points R and the planes is `(20/sqrt6)pi` cubic units. (d) The area of the curved surface formed by the set of points R is `(10/sqrt3)pi` sq. units

Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise ARCHIVES INTEGER TYPE|1 Videos

Similar Questions

Explore conceptually related problems

Find the angle between the planes 3x+y+2z=1 and 2x-y+z+3 = 0 .

Find the points of intersection of the line (x-2)/(-3)=(y-1)/2=(z-3)/2 and the plane 2x+y-z=3 .

Find the distance between the line (x+1)/(-3)=(y-3)/2=(z-2)/1 and the plane x+y+z+3=0.

Find the distance between the line (x+1)/(-3)=(y-3)/2=(z-2)/1 and the plane x+y+z+3=0.

The disatance of the point (1, 0, 2) from the point of intersection of the line (x-2)/(3)=(y+1)/(4)=(z-2)/(12) and the plane x-y+z=16 , is

A perpendicular is drawn from a point on the line (x-1)/(2)=(y+1)/(-1)=(z)/(1) to the plane x+y+z=3 such that plane x-y+z=3. Then, the coordinates of Q are

A perpendicular is drawn from a point on the line (x-1)/(2)=(y+1)/(-1)=(z)/(1) to the plane x+y+z=3 such that plane x-y+z=3. Then, the coordinates of Q are

Find the co-ordinates of the point at a distance of sqrt(5) units from the point (1,2,3) on the line (x+2)/(3) = (y+1)/(2) = (z-3)/(2) .

Find the distance of the point (2, 3, 4) from the line (x+3)/3=(y-2)/6=z/2 measured parallel to the plane 3x + 2y + 2z - 5= 0 .

The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve x^2+y^2=r^2, z=0 , then

CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions
  1. Let P(3,2,6) be a point in space and Q be a point on line vec r=( hat...

    Text Solution

    |

  2. If the lines (x-1)/2=(y+1)/3=(z-1)/4 and (x-3)/1=(y-k)/2=z/1 intersec...

    Text Solution

    |

  3. Consider a set of point R in which is at a distance of 2 units from t...

    Text Solution

    |

  4. Let L be the line of intersection of the planes 2x""+""3y""+""z""=""...

    Text Solution

    |

  5. Statement 1: A plane passes through the point A(2,1,-3)dot If dista...

    Text Solution

    |

  6. Consider the following linear equations: a x+b y+c z=0 b x+c y+a z=0 c...

    Text Solution

    |

  7. If the distance between the plane Ax-2y+z=d. and the plane containing ...

    Text Solution

    |

  8. Prove that the volume of tetrahedron bounded by the planes vec rdo...

    Text Solution

    |

  9. If a variable plane forms a tetrahedron of constant volume 64k^3 with ...

    Text Solution

    |

  10. O A ,O Ba n dO C ,w i t hO as the origin, are three mutually perpen...

    Text Solution

    |

  11. Prove that for all values of lambda and mu , the planes (2x)/a+y/b+(...

    Text Solution

    |

  12. If P is any point on the plane l x+m y+n z=pa n dQ is a point on the l...

    Text Solution

    |

  13. find the equation of the plane with intercepts 2,3 and 4 on the x, y a...

    Text Solution

    |

  14. A variable plane l x+m y+n z=p(w h e r el ,m ,n are direction cosines ...

    Text Solution

    |

  15. P is a point and P Ma n dP N are the perpendicular form Ptoz-xa n dx-y...

    Text Solution

    |

  16. Let a plane a x+b y+c z+1=0,w h e r ea ,b ,c are parameters, make an ...

    Text Solution

    |

  17. Let x-ysin alpha-zsin beta=0,xsin alpha+zsin gamma-y=0 and xsin beta+y...

    Text Solution

    |

  18. The position vectors of the four angular points of a tetrahedron OABC ...

    Text Solution

    |

  19. Find the distance of the point (-2,3,-4) from the line ("x"+2)/3=(2"...

    Text Solution

    |

  20. The plane 4x+7y+4z+81=0 is rotated through a right angle about its ...

    Text Solution

    |