Home
Class 12
MATHS
Distance of point P(-2,3,4) from the lin...

Distance of point `P(-2,3,4)` from the line `(x+2)/3=(2y+3)/4=(3z+4)/5` measured parallel to the plane `8x+6y-9z+1=0` is

A

`(sqrt(301))/2`

B

`(sqrt(401))/2`

C

`(sqrt(307))/2`

D

`(sqrt(207))/2`

Text Solution

Verified by Experts

The correct Answer is:
B
`(x+2)/3=(y+3/2)/2=(z+4/3)/(5/3)=lamda`…………(1)
`P(-2,3,4)`
any variable point on line (1) `A(3lamda-2,2lamda-3/2, 5/3lamda-4/3)`
no line `AP` and normal of given plane are perpendicular
`implies (3lamda)8+((4lamda-9)/2)6+((5lamda-16)/3)(-9)=0`
`implieslamda=-1`
Distance `=sqrt(401)/2`
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Find the distance of the point (-2,3,-4) from the line (x+2)/(3)=(2y+3)/(4)=(3z+4)/(5) measured parallel to the plane 4x+12y-3z+1=0

The distance of the point P(-2, 3, -4) from the line (x+2)/(3)=(2y+3)/(4)=(3z+4)/(5) measured parallel to the plane 4x+12y-3z+1=0 is d, then find the value of (2d-8), is……..

Find the distacne of the point (2,3,-4) from the line (x+2)/(3)=(2y+3)/(4)=(3z+4)/(5) measured paralle to the plane 4x+12y-3z+1=0

The distance of the point P(3,8,2) from the line (x-1)/(2)=(y-3)/(4)=(z-2)/(3) measured parallel to the plane 3x+2y-2z+17=0 is

(i) Find the distance of the point (-2,3,-4) from the line : (x + 2)/(3) = (2y + 3)/(4) = (3z + 4)/(5), measured parallel to the plane 4x +12y -3z +1 = 0. (ii) Find the distance of the point -2hati+3hatj-4hatk from the line : vecr=hati+2hatj-hatk+lambda(hati+3hatj-9hatk) measured parallel to the plane x-y+2z-3=0

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

If the distance of point P(3, 2, 6) from the line (x-1)/(2)=(y-2)/(3)=(z-3)/(4) measured parallel to the plane 3x-5y+2z=5 is k, then then the value of k^(2) is equal to

Find the distance of the point P(3,8,2) from the line (1)/(2)(x-1)=(1)/(4)(y-3)=(1)/(3)(z-2) measured parallel to the plane 3x+2y-2z+15=0

RESONANCE-TEST PAPERS-MATHEMATICS
  1. P is a variable point on the ellipse x^2/a^2+y^2/b^2=2\ (a gt b) whose...

    Text Solution

    |

  2. The general solution of |sinx|=cosx is (When ninz) given by

    Text Solution

    |

  3. Distance of point P(-2,3,4) from the line (x+2)/3=(2y+3)/4=(3z+4)/5 me...

    Text Solution

    |

  4. The point P(1,1,1) is transiated parallel to 2x=yin the first quadrant...

    Text Solution

    |

  5. A function f from integers to integers is defined as f(x)={(n+3, n "is...

    Text Solution

    |

  6. If f(x)=x^(n),"n" epsilon N, then the value of f(1)-(f^(')(1))/(1!)+(f...

    Text Solution

    |

  7. The extremities of the diagonal of a rectangle are (-4, 4) and (6,-1)....

    Text Solution

    |

  8. In a city no two persons have identical set of teeth and there is n...

    Text Solution

    |

  9. The number of values of k for which the system of equations: kx+(3k+...

    Text Solution

    |

  10. The probability that the graph of y=16x^2 +8(a +5)x-7a-5=0, is strictl...

    Text Solution

    |

  11. If ,Z1,Z2,Z3,........Z(n-1) are n^(th) roots of unity then the value ...

    Text Solution

    |

  12. Let f(x)=int(2)^(x)(dt)/(sqrt(1+t^(4))) and g be the inverse of f then...

    Text Solution

    |

  13. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

    Text Solution

    |

  14. Let f(x)=lim(nrarroo)1/((3/(pi)tan^(-1)2x)^(2n)+5) then the set of val...

    Text Solution

    |

  15. Area bounded by the region R-={(x,y):y^(2)lexle|y|} is

    Text Solution

    |

  16. The range of the function, f(x)= (1+sec^-1x) (1 + cos^-1 x) is

    Text Solution

    |

  17. If a, b, c are distinct odd integers and omega is non real cube root o...

    Text Solution

    |

  18. Consider the following equation in x and y: (x-2y-1)^2 + (4x+3y-4)^2 +...

    Text Solution

    |

  19. If f(n)=int(0)^(2015)(e^(x))/(1+x^(n))dx, then find the value of lim(n...

    Text Solution

    |

  20. ~(~p to q) is equivalent to

    Text Solution

    |