Show that the distance of the point of intersection of the line `(x-2)/3=(y+1)/4=(z-2)/12` and the plane `(x-y+z=5)` from the point `(-1,-5,-10)` is 13 units.

Answer

`(x-4)/1=(y-6)/2=(z-2)/2`

Explanation

Given line is `(x-2)/3=(y+1)/4=(z-2)/12=lambda` (say)
A general point on this line is `P(3lambda+2,4lambda-1,12lambda+2)`.
If this point is `P(2,-1,2)` and the other points is `Q(-1,-5,-10)`.
`therefore PQ =13` units.