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Question

Find the co-ordinates of those points on the line x12=y+23=z36 which is at a distance of 3 units from point (1,2,3).

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Solution

Given line,
x12=y+23=z36
Hence point of the line satisfy the condition,
x12=y+23=z36=R
or,(x,y,z)=(2k+1,3R2,6R+3)......(i)
(where R is a constant)
Now, if distance between a point on the line and a point (1,2,3) is 3 unit, then we have
(2R+11)2+(3R2+2)2+(6R+33)2=3......(ii)
Solving the above equation for R.
We get R=37
Now,
From (i) we get the coordinates of required point as (137,57,397)

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