A plane passes through a fixed point `(a ,b ,c)dot` Show that the locus of the foot of the perpendicular to it from the origin is the sphere `x^2+y^2+z^2-a x-b y-c z=0.`

Explanation

To show that the locus of the foot of the perpendicular from the origin to a plane passing through a fixed point \((a, b, c)\) is given by the equation of the sphere \(x^2 + y^2 + z^2 - ax - by - cz = 0\), we can follow these steps:

### Step 1: Define the Plane
Let the equation of the plane passing through the point \((a, b, c)\) be given by:
\[ Ax + By + Cz + D = 0 \]
Since the plane passes through the point \((a, b, c)\), we can substitute these coordinates into the plane equation to find \(D\):
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