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Consider three non-collinear points.

The goal is to demonstrate why it determines a unique plane and how to obtain the plane's equation from three non-collinear locations.

The three non-collinear points serve as the triangle's vertices, which are utilized to draw the plane containing the points.

As a result, a unique plane is determined by the three non-collinear points.

To obtain the equation of the plane from three non-collinear locations $P,Q$and $R$follow the procedures below.

• Construct the vectors $\stackrel{鈫�}{PQ}$and $\stackrel{鈫�}{PR}$
• Find the normal vector $\mathbf{N}=鉄�a,b,c鉄�$by the relation $\mathbf{N}=\stackrel{鈫�}{PQ}脳\stackrel{鈫�}{PR}$
• Use $\mathbf{N}=鉄�a,b,c鉄�$and point $P$ to find the equation of the plane.

Because three collinear points identify an infinite number of planes, they do not determine a single plane. Several aircraft can pass through the same line at the same time. As a result, collinear points do not determine the existence of a single plane.