Solve for Equation of a Plane in 3 Space

Find the equation of a plane through three points in x, y, z space. You will enter three points: P(x,y,z), Q(x,y,z), and R(x,y,z). Standard form for a Cartesian equation of a plane is as follows:

a x + b y + c z + d = 0

P:(x,y,z) = P(x) P(y) P(z)
Q:(x,y,z) = Q(x) Q(y) Q(z)
R:(x,y,z) = R(x) R(y) R(z)

Plane Equation (point-normal form) :

Plane Equation (standard form) :

Vector Representation of Directed Line Segments PQ and PR

Directed Line Segment PQ (Vector a):
Directed Line Segment PR (Vector b):

Cross Product a x b

The cross product a x b is a vector that is perpendicular to both a and b and thus to the plane represented by directed line segments PQ and PR.

Cross Product a x b:

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