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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.`

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To solve the problem, we need 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 a sphere: \[ x^2 + y^2 + z^2 - ax - by - cz = 0. \] ### Step-by-Step Solution: ...
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