Home
Class 12
MATHS
Prove that for all values of lambda an...

Prove that for all values of `lambda` and `mu` , the planes `(2x)/a+y/b+(2z)/c-1+lambda(x/a-(2y)/b-z/c-2)=0` and `(4x)/a-(3y)/b-5+mu((5y)/b+(4z)/c+3)=0` intersect on the same line.

Text Solution

AI Generated Solution

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

The lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-1)/3=(y-2)/4=(z-3)/5 are (A) parallel to x-axis (B) skew (C) intersecting (D) none of these

If the lines (x-1)/(1)=(y-3)/(1)=(z-2)/(lambda) and (x-1)/(lambda)=(y-3)/(2)=(z-4)/(1) intersect at a point, then the value of lambda^(2)+4 is equal to

For which value of "lambda" ,planes "4x+6y-2z=8" and "2x+3y+lambda z=12" are parallel?

The system of linear equations x + y + z = 0 (2x)/(a) + (3y)/(b) + (4z)/(c ) = 0 (x)/(a) + (y)/(b) + (z)/(c ) = 0 has non trivia solution then

If the lines (x-3)/(2)=(y-5)/(2)=(z-4)/(lambda) and (x-2)/(lambda)=(y-6)/(4)=(z-5)/(2) intersect at a point (alpha, beta, gamma) , then the greatest value of lambda is equal to

If theta is the angel between the planes 2x-y+z-1=0 and x-2y+z+2=0 then costheta= (A) 2/3 (B) 3/4 (C) 4/5 (D) 5/6

A plane through the line (x-1)/1=(y+1)/(-2)=z/1 has the equation (A) x+y+z=0 (B) 3x+2y-z=1 (C) 4x+y-2z=3 (D) 3x+2y+z=0

The planes 2x + 5y + 3z = 0, x-y+4z = 2 and7y-5z + 4 = 0

If a^x=b^y=c^z and b^2=a c , then show that y=(2z x)/(z+x)

The equation of the plane which is equally inclined to the lines (x-1)/2=y/(-2)=(z+2)/(-1)a n d=(x+3)/8=(y-4)/1=z/(-4) and passing through the origin is/are a. 14 x-5y-7z=0 b. 2x+7y-z=0 c. 3x-4y-z=0 d. x+2y-5z=0

CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions
  1. If a variable plane forms a tetrahedron of constant volume 64k^3 with ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. If (a, b, c) is a point on the plane 3x + 2y + z = 7, then find the ...

    Text Solution

    |

  14. Let the equation of the plane containing the line x-y - z -4=0=x+y+ 2z...

    Text Solution

    |

  15. Let a1, a2, a3.......... be in A.P. and h1,h2,h3.....,in H.P. If a1=2 ...

    Text Solution

    |

  16. If the angle between the plane x-3y+2z=1 and the line (x-1)/2=(y-1)/...

    Text Solution

    |

  17. The length of projection of the line segment joining the points (1,...

    Text Solution

    |

  18. Find the equation of a plane passing through (1, 1, 1) and parallel to...

    Text Solution

    |

  19. Find the equation of the plane passing through the points(2,1,0),(5,0,...

    Text Solution

    |

  20. For the line (x-1)/(1)=(y-2)/(2)=(z-3)/(3), which one of the following...

    Text Solution

    |