How to calculate the equation of a plane passing through three points?
To find the equation of a plane passing through three given points in 3D, let the three points be A(x 1 , y 1 , z 1 ), B(x 2 , y 2 , z 2 ), and C(x 3 , y 3 , z 3 ). First, calculate two vectors lying in the plane, say AB = (x 2 - x 1 , y 2 - y 1 , z 2 - z 1 ) and AC = (x 3 - x 1 , y 3 - y 1 , z 3 - z 1 ). Then, find the cross product of these vectors to get the normal vector n to the plane. The equation of the plane is then given by:
n · (r - r ? ) = 0
where r is a point on the plane, (r - r ? ) is a known point (such as A ), and n is the normal vector obtained from the cross-product.
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