Home
Class 12
MATHS
Let P(1): x+y+z=0 P(2)x+2y+3y=0 P(3...

Let `P_(1): x+y+z=0`
`P_(2)x+2y+3y=0`
`P_(3): x+3y+5z=0` be three planes
`L_(1)` is the line of intersection of `P_(1) & P_(2)`
Let `P(2,1-1)` be point on `P_(3)` If `(alpha,beta,lambda)` is image of point P in line `L_(1)` then value of `|alpha + beta+ lambda|` is

Text Solution

Verified by Experts

The correct Answer is:
2
Direction ratio of line `L_(1)` is `|(hat(i),hat(j),hat(k)),(1,1,1),(1,2,3)|`
therefore Line `L_(1):(x)/(1)=(y)/(-2)=(z)/(1)`

`(lambda-2)-2(-2lambda-1)+(lambda+1)1=0`
`6lambda=-1implies lambda=(-1)/(6)`
`(alpha+2)/(2)=lambda,(beta+1)/(2)=-2lambda,(lambda-1)/(2)=lambda`
`implies alpha+beta+lambda=-2-1+1+2lambda-41+2lambda=-2`
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Let P_(1)=x+y+z+1=0, P_(2)=x-y+2z+1=0,P_(3)=3x+y+4z+7=0 be three planes. Find the distance of line of intersection of planes P_(1)=0 and P_(2) =0 from the plane P_(3) =0.

Let P_(1) : 2x + y + z + 1 = 0 P_(2) : 2x - y + z + 3 = 0 and P_(3) : 2x + 3y + z + 5 = 0 be three planes, then the distance of the line of intersection of planes P_(1) = 0 and P_(2) = 0 from the plane P_(3) = 0 is

Let L be a line obtained from the intersection of two planes x+2y+z = 6 and y+2z=4 . If point P(alpha,beta,gamma) is the foot of perpendicular from (3,2,1) on L then the value of 21(alpha+beta+gamma) equals .

Let two planes p _(1): 2x -y + z =2 and p _(2) : x + 2y - z=3 are given : equation of the plane through the intersection of p _(1) and p_(2) and the point (3,2,1) is :

Let (2,-1) be the point P and x- y + 1 =0 be the straight line l. If Q is image of point P about line, that image of point Q about y-axis is

P_(1) : x + 3y - z = 0 and P_(2) , y + 2z = 0 are two intersecting planes P_(3) is a plane passing through the point (2,1,-1) and through the line of intersection of P_(1) and P_(2) Equation of P_(3) is

P_(1) : x + 3y - z = 0 and P_(2) : y + 2z = 0 are two intersecting planes P_(3) is a plane passing through the point (2,1,-1) and through the line of intersection of P_(1) and P_(2) __________ is a point on P_(3) .

P_(1) : x + 3y - z = 0 and P_(2) : y + 2z = 0 are two intersecting planes P_(3) is a plane passing through the point (2,1,-1) and through the line of intersection of P_(1) and P_(2) Distance of P_(3) from origin is _______ units.

In R^(3) , consider the planes P_(1):y=0 and P_(2),x+z=1. Let P_(3) be a plane, different from P_(1) and P_(2) which passes through the intersection of P_(1) and P_(2) , If the distance of the point (0,1,0) from P_(3) is 1 and the distance of a point (alpha,beta,gamma) from P_(3) is 2, then which of the following relation(s) is/are true?

Let P_(1):x-2y+3z=5 and P_(2):2x-3y+z+4=0 be two planes. The equation of the plane perpendicular to the line of intersection to the line of intersection of P_(1)=0 and P_(2)= and passing through (1,1,1) is

ALLEN-TEST PAPERS-part-2 Mathematics
  1. The number of points in the domain of 'f' where f(x)=|x^(2)-4x+3| s...

    Text Solution

    |

  2. Let L(1):x=y=z L(2): x-1=y-2=z-3 be two lines Let from origin O(...

    Text Solution

    |

  3. Let P(1): x+y+z=0 P(2)x+2y+3y=0 P(3): x+3y+5z=0 be three planes ...

    Text Solution

    |

  4. A(x(1),y(1)) and B(x(2),y(2)) are any two distinct points on the parab...

    Text Solution

    |

  5. If f:R rarr R is continuous function satisfying f(0) =1 and f(2x) -f(...

    Text Solution

    |

  6. Consider the parabola y^(2)=8x, if the normal at a point P on the par...

    Text Solution

    |

  7. Tangents, parallel to angle bisector of lines lx+my+n=0 and ax +by +c...

    Text Solution

    |

  8. The equations of the transverse and conjugate axes of a hyperbola are...

    Text Solution

    |

  9. The locus of the midde points ofchords of hyperbola 3x^2-2y^2+4x -6y=0...

    Text Solution

    |

  10. Let f(x) =x^(2)-3x+2 g(x)=f(|x|) h(x)=|g(x)| are three functions...

    Text Solution

    |

  11. vec(a) "and" vec(b) are two given mutually perpendicular vectors such...

    Text Solution

    |

  12. Find the least value of k such that the equation (ln x) + k = e^(x-k) ...

    Text Solution

    |

  13. Volume of tetrahedron formed by the planes x+y=0, y+z=0, z+x=0,x+y+z-1...

    Text Solution

    |

  14. If f' ((x)/(y)), f(x)/(y))=(x^(2)+y^(2))/(xy) AA x,y in R^(+) and f(1)...

    Text Solution

    |

  15. Range of the function f defined by (x) =[(1)/(sin{x})] (where [.] an...

    Text Solution

    |

  16. The value of sqrt3cot20^(@)-4cos20^(@) is

    Text Solution

    |

  17. Which of the following function is surjective but not injective?

    Text Solution

    |

  18. f:RrarrR is a function satisfying f(x+5)gef(x)+5 and f(x+1)lef(x)+1. ...

    Text Solution

    |

  19. If f(x)=((1-tanx)/(1+sinx))^(cosec x) is to be made continuous at x=0,...

    Text Solution

    |

  20. If a(1) is the greatest value of f(x) , where f(x) =((1)/(2+[sinx])) (...

    Text Solution

    |