Home
Class 12
MATHS
The equation of plane passing through th...

The equation of plane passing through the point `hati+hatj+hatk` and paralel to the plane `vecr.(2hati-hatj+2hatk)=5` is

A

`vecr.(2hati-hatj+2hatk)=5`

B

`vecr.(2hati-hatj+2hatk)=-3`

C

`vecr.(2hati-hatj+2hatk)=3`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
The equation of a plane parallel to the plane `vecr.(2hati-hatj+2hatk)=5` is
`vecr.(2hati-hatj+2hatk)=d`…………….i
Since it passes through `hati+hatj+hatk`.
`:.(hati+hatj+hatk).(2hati-hatj+2hatk)=dimplies2-1+2=d=d=3`.
Putting `d=3` in i we obtain `vecr.(2hati-hatj+2hatk)=3`
This is the equation of the required plane.
Promotional Banner

Topper's Solved these Questions

  • PLANE AND STRAIGHT LINE IN SPACE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|89 Videos

  • PLANE AND STRAIGHT LINE IN SPACE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|16 Videos

  • MISCELLANEOUS EQUATIONS AND INEQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|55 Videos

Similar Questions

Explore conceptually related problems

Write the vector equation of the plane passing through the point (a, b,c) and parallel to the plane vecr. (hati + hatj + hatk) = 2.

Find the equation of a line passing through the point (2hati-3hatj-5hatk) and perpendicular to the plane vecr.(6hati-3hatj+5hatk) +2=0 . Also find the point of intersection of this line and the plane.

Find the equation of the plane passing through the point hati-hatj+hatk and perpendicular to the vectro 3hati-hatj-2hatk and show that the point 2hati+4hatj lies on the plane.

Find the equation of a line passing through the point (1,2,3) and perpendicular to the plane vecr.(2hati-3hatj+4hatk) = 1 .

Find the equation of the plane passes through the point (2,1,-2) and parallel to the plane vecr.(3hati+hatj-hatk) = 0 .

Find the vector equation to the plane through the point -hati+3hatj+2hatk perpendicular to each of the planes vecr.(hati+2hatj+2hatk)=25 and vecr.(3hati+3hatj+2hatk)=8.

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes vecr*(hati-hatj+2hatk)=5 and vecr*(3hati+hatj+hatk)=6 .

The vector equation of the plane passing through the points hati+hatj-2hatk,2hati-hatj+hatk and hati+hatj+hatk , is

Find the equation of the plane passing through (a,b,c) and parallel through plane vecr.(hati+hatj+hatk)=2 .

Find the equation of a plane passing through the intersection of the planes vecr . (hati+3hatj-hatk) = 5 and vecr.(2hati-hatj+hatk) = 3 and passes through the point (2,1,-2) .

OBJECTIVE RD SHARMA ENGLISH-PLANE AND STRAIGHT LINE IN SPACE -Chapter Test
  1. The equation of plane passing through the point hati+hatj+hatk and par...

    Text Solution

    |

  2. The length of the perpendicular from the origin to the plane passing t...

    Text Solution

    |

  3. The value of lamda for which the lines (x-1)/1=(y-2)/(lamda)=(z+1)/(-1...

    Text Solution

    |

  4. The angle between the lines (x+4)/(1) = (y-3)/(2) = (z+2)/(3) and (x)/...

    Text Solution

    |

  5. The direction cosines of the line 6x-2=3y+1=2z-2 are

    Text Solution

    |

  6. A line passes through two points A(2,-3,-1) and B(8,-1,2). The coordin...

    Text Solution

    |

  7. The position vector of a point at a distance of 3sqrt(11) units from h...

    Text Solution

    |

  8. The line joining the points 6veca-4vecb+4vecc, -4vecc and the line joi...

    Text Solution

    |

  9. The image (or reflection) of the point (1,2-1) in the plane vecr.(3hat...

    Text Solution

    |

  10. The equation of the plane through the line of intersection of the plan...

    Text Solution

    |

  11. Angle between the line vecr=(2hati-hatj+hatk)+lamda(-hati+hatj+hatk) a...

    Text Solution

    |

  12. The line through hati+3hatj+2hatkandbot"to the line "vecr=(hati+2hatj-...

    Text Solution

    |

  13. The distance of the point having position vector -hat(i) + 2hat(j) + 6...

    Text Solution

    |

  14. The position vector of the point in which the line joining the points ...

    Text Solution

    |

  15. The two lines vecr=veca+veclamda(vecbxxvecc) and vecr=vecb+mu(veccxxve...

    Text Solution

    |

  16. Lines vecr = veca(1) + lambda vecb and vecr = veca(2) + svecb will lie...

    Text Solution

    |

  17. Equation of a line passing through (-1,2,-3) and perpendicular to the ...

    Text Solution

    |

  18. Find the Vector and Cartesian equation of line passing through (1, -2,...

    Text Solution

    |

  19. The distance between the planes given by vecr.(hati+2hatj-2hatk)+5=0...

    Text Solution

    |

  20. Find shortest distance between the line vecr = (5hati + 7hatj + 3ha...

    Text Solution

    |

  21. Find the shortest distance between the lines vecr=(hatii+2hatj+hatk)+l...

    Text Solution

    |