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Find the Normal vector of plane

Calculate the normal unit vector of a face or plane

To derived the normal unit vector n of a plane/face, we can use any two vectors that lie on the plane.

PQ and PS in this example

		Q_x - P_x
PQ =		Q_y - P_y
		Q_z - P_z

		S_x - P_x
PS =		S_y - P_y
		S_z - P_z

		( PQ_y × PS_z ) - ( PQ_z × PS_y )
The normal vector n =		( PQ_z × PS_x ) - ( PQ_x × PS_z )
		( PQ_x × PS_y ) - ( PQ_y × PS_x )

		( (Q_y - P_y) × (S_z - P_z) ) - ( (Q_z - P_z) × (S_y - P_y) )
The normal vector n =		( (Q_z - P_z) × (S_x - P_x) ) - ( (Q_x - P_x) × (S_z - P_z) )
		( (Q_x - P_x) × (S_y - P_y) ) - ( (Q_y - P_y) × (S_x - P_x) )

To calculate the unit vector:

First calculate the length of the normal vector

l = √( n_x² + n_y² + n_z² )

		n_x / l
The unit vector n =		n_y / l
		n_z / l

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