Home
Class 12
MATHS
The equation of the plane passing throug...

The equation of the plane passing through the points (1,2,3), (-1,4,2) and (3,1,1) is

A

5x+y+12z-23=0

B

5x+6y+2z-23=0

C

`x+6y+2z-13=0`

D

`x+y+z-13=0`

Text Solution

Verified by Experts

The correct Answer is:
B
Equation of plane through
(1,2,3) is
`a(x-1)+b(y-2)+c(z-3)=0` . . (i)
It passes through (-1,4,2)
and (3,1,1).
`therefore-2a+2b-c=0` . . . (ii)
and `2a-b-2c=0` . . . (iii)
From eqs. (ii) and (iii), we get
`(a)/(-5)=(b)/(-6)=(c)/(-2)`
`therefore` Equation of plane is
`-5x-6y-2z+5+12+6=0`
`implies5x+6y+2z-23=0`
Promotional Banner

Topper's Solved these Questions

  • PRACTICE SET 09

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 2 (MATHEMATICS)|50 Videos

  • PRACTICE SET 11

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 2 (MATHEMATICS )|50 Videos

Similar Questions

Explore conceptually related problems

Equation of the plane passing through the points (1,0,1), (-1,1,1) and (2,3,1) is

The equation of plane passing through the points (1,2,-3),(3,1,0) and (0,1,1) is

The vector equation of the plane passing through the points (1,-2,1),(2,-1,-3) and (0,1,5) is

vector equation of the plane passing through the points (1,-2,5),(0,-5,-1) and (-3,5,0) is

The equation of the plane passing through the points A(2,3,-1) B(4,5,2) C(3,6,5) is

The cartesian equation of the plane passing through the points (1 ,1,2),(0,2,3) and(4,5,6) is

Find the equation of the plane passing through the points (0,-1,-1), (4,5,1) and (3,9,4). Also find the vector equation of the plane.

Find the vector equation of the plane passing through the points (1,1,0),(1,2,1) and (-2,2,-1)

Find the vector equation of the plane passing through the points (1, 1, 1), (2, 4, 3) and (5,9,7).

Which of the following are equation for the plane passing through the points P(1,1,-1),Q(3,0,2)and (-2,1,0) ?

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 10-PAPER 2 (MATHEMATICS)
  1. Solution of y dx - x dy = x^(2)ydx is

    Text Solution

    |

  2. The second order derivative of a sin^3 t w.r.t, a cos^3 t at t = pi/4...

    Text Solution

    |

  3. The equation of the plane passing through the points (1,2,3), (-1,4,2)...

    Text Solution

    |

  4. To maximise the objective function z=x+2y under the constraints x-y le...

    Text Solution

    |

  5. If (sin(x+y))/(sin(x-y))=(a+b)/(a-b) , then show that (tanx)/(tany)=(...

    Text Solution

    |

  6. If the equation lamdax^(2)+(2lamda-3)y^(2)-4x-1=0 represents a circle,...

    Text Solution

    |

  7. If the lines joining the origin to the points of intersection of the ...

    Text Solution

    |

  8. The distance between the foci of the conic 7x^(2)-9y^(2)=63 is equal t...

    Text Solution

    |

  9. The line l x+m y+n=0 is a normal to the ellipse (x^2)/(a^2)+(y^2)/(...

    Text Solution

    |

  10. The angle of intersection of the curves y=x^(2)andx=y^(2) at (1,1) is

    Text Solution

    |

  11. A straight line passing through the point(2,2) and the axes enclose an...

    Text Solution

    |

  12. If a committee of 3 is to be chosen from a group of 38 people of which...

    Text Solution

    |

  13. The real number x when added to its inverse given the minimum value of...

    Text Solution

    |

  14. The value of underset(xto2)(e^(3x-6)-1)/(sin(2-x))

    Text Solution

    |

  15. If f(x)=3x^(4)+4x^(3)-12x^(2)+12, then f(x) is

    Text Solution

    |

  16. In which of the following functions, Rolle's theorem is applicable?

    Text Solution

    |

  17. An edge of a variable cube is increasing at the rate of 10cm/sec. How ...

    Text Solution

    |

  18. The general solution of y^(2)dx+(x^(2)-xy+y^(2))dy=0, is

    Text Solution

    |

  19. cos{cos^(-1)(-1/7)+sin^(-12)(-1/7)} =

    Text Solution

    |

  20. In any triangle ABC, if a=\ 18 , b=\ 24 , c=\ 30, findsinA, sinB, sinC

    Text Solution

    |