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Analytical Geometry
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The fool-proof solution for this question is as follows-
1. Find the equation of the plane which is parallel to the given plane and passes through given point.
2. find the point where this plane cuts the given line.
3. Find the distance between the point obtained and the given point. this distance is the answer required.
It is a tidious task Jayant... I hav faced a similar sum in my half-yearly..It takes lots of time coz usually the points that u get will be in fraction.. to square and to take square root will be a enormous job... Best way to do is to use dot product!!
Q. Find the distane of point ( -2,3,-4) form the line x+2 / 3 = 2y+3 / 4 = 3z-4 / 5 measured along the plane 4x+12y -3z = 11 ??
well, here's my attempt :
im assuming dat u meant d divided by thing fr d whole thing in ur line eqn .....
(x + 2 ) / 3 = ( y + 3/2 )/ 2 = ( z - 4/3 ) / 5/3 = K
so let pt. on line be A ( 3K - 2 , 2K - 3/2 , 5K/3 + 4/3 )
and let B be ( -2, 3, -4 )
dr of AB = ( 3K, 2K - 9/2 , 5K/3 +16/3 )
now, u r given dat Ab is measured along d plane 4x+12y -3z = 11 ....
so Ab is perpendicular 2 normal 2 plane
and normal has dr ( 4, 12, -3 )
so sum of product of drs = 0
and u get 3K*4 + 12*( 2K - 9/2) + -3 * ( 5K/3 +16/3) = 0
find K
get d point
use distance formula ....
JOB DONE !! 
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soory here is the Q...
Find the distane of point ( -2,3,-4) form the line x+2 / 3 = 2y+3 / 4 = 3z-4 / 5 measured alone the plane 4x+12y -3z = 11 ???