a) Prove that the equation of any plane in space can be written in the form b1x + b2y + b3z =c. (Hint: Prove that the dot product of the position vector to any point in the plane and a normal vector is a constant.)
b) Find the expression for the unit normal passing through the origin.
c) For the plane 3x - 2y + 6z = 5, find the perpendicular distance from the origin to the plane.
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