# 4  In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin.    (d)      5y + 8 = 0

Let the coordinates of the foot of perpendicular P from the origin to the plane be

Given plane equation .

or written as

The direction ratios of the normal of the plane are .

Therefore

So, now dividing both sides of the equation by  we will obtain,

This equation is similar to  where,  are the directions cosines of normal to the plane and d is the distance of normal from the origin.

Then finding the coordinates of the foot of the perpendicular are given by

The coordinates of the foot of the perpendicular are;

or  .

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