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Equation of a Plane - 3 Points
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Main Concept
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A plane can be defined by four different methods:
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A line and a point not on the line
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Three non-collinear points (three points not on a line)
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A point and a normal vector
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Two parallel and non-coincident lines
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The Cartesian equation of a plane is  , where  is the vector normal to the plane.
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How to find the equation of a plane using three non-collinear points 
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Three points (A,B,C) can define two distinct vectors AB and AC. Since the two vectors lie on the plane, their cross product can be used as a normal to the plane.
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2.
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Find the cross product of the two vectors
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3.
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Substitute one point into the Cartesian equation to solve for d.
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Example:
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Find the equation of the plane that passes through the points  .
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2.
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Determine the normal vector
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3.
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The equation of the plane is:
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4.
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Plug in any point to find the value of d
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5.
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The equation of the plane is 
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Change the three points on the plane and see how it affects the plane.
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