Q. The coordinates of the foot of perpendicular drawn from origin to the plane is

 1773  190 Three Dimensional Geometry Report Error

Solution:

Let the coordinates of the foot of the perpendicular from the origin to the plane is .

image

Then, the direction ratios of the line are , , .
Writing the equation of the plane in the normal form, we
have
where, , , are the direction cosines of the lines .
Since, . and . of a line are proportional. Then, we
have
i.e., ,
,

Substituting these values in the equation of the plane,
we get

Hence, the foot of the perpendicular is .