Let the coordinates of the foot of the perpendicular P from the origin to the plane is (x1,y1,z1).
Then, the direction ratios of the line OP are x1, y1, z1.
Writing the equation of the plane in the normal form, we
have 292x−293y+294z=296
where, 292, 29−3, 294 are the direction cosines of the lines OP.
Since, d.c′s and d.r′s of a line are proportional. Then, we
have 292x1=29−3y1=294z1=k
i.e., x1=292k, y1=29−3k, z1=294k
Substituting these values in the equation of the plane,
we get 294k+299k+2916k−6=0 ⇒k=296
Hence, the foot of the perpendicular is (2912,29−18,2924).