Equation of a Plane - Point and a Normal - Maple Help

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Equation of a Plane — Point and a Normal

Main Concept

A plane can be defined by five different methods:

 • A line and a point not on the line
 • Three non-collinear points (three points not on a line)
 • A point and a normal vector
 • Two intersecting lines
 • Two parallel and non-coincident lines

The Cartesian equation of a plane π is , where is the vector normal to the plane.

How to find the equation of the plane through a point with a given normal vector

Let  be the point and  be the normal vector.

 1 Substituteinto  respectively.
 2 Plug in point P and solve for the last unknown variable d.

Example:

Find the equation of the plane that passes through the point  with a normal vector

 1 Substitute  into  respectively



 2 Plug in point P and solve for the last unknown variable d.



 ${\mathrm{π}}_{}:$ $=$ $0$  $=$ $0$  $d$ $=$ $-9$

 3 The equation of the plane is 

Change the point and the normal see how it affects the plane.

 Point A Normal $x=$ $y=$ $y=$ $z=$ $z=$



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