# Find the vector and cartesian equations of the plane passing through the points having position vectors Write the equation of a plane passing through a point and parallel to the plane obtained above. Hence, find the distance between the two parallel planes.

Let A,B,C be the points with the position vectors respectively.

Then , A vector normal to the plane containing points A, B and C is The required plane passes through the point having vector and is normal to the vector . So its vector equation is This is the required vector equation of the plane the cartesian equation of plane is given by Direction ratios of this plane are then the equation of the plane parallel to the above plane and passing through is This is the required parallel plane

Then, Distance between Let be any point on Then, Let d be the distance between planes. Then,

d = length of perpendicular from to  ## Related Chapters

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