it seems that you have missed the z part of the plane.
if the equation of the plane is 3x+2y-2z+15=0 then the answer to your query is as follows:
draw a line through P(3,8,2) parallel to the plane 3x+2y-2z15=0.
suppose it cuts the line
At point N(2r+1 , 4r+3 , 3r+2).
direction ratio of PN are proportional to 2r+1-3 , 4r+3-8 , 3r+2-2 i.e 2r-2 , 4r-5 , 3r.
Since PN is parallel to the plane 3x+2y-2z+15=0. so, it is perpendicular to the normal to the plane.
consequently, we have:
