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4.2. Plane in space

Lecture



Let given PDK. The equation   4.2.  Plane in space sets the plane and is called the general equation of the plane. To write a general equation of the plane, it is necessary to determine the normal vector   4.2.  Plane in space (the normal of the plane is a straight line perpendicular to the plane) and one point of the plane   4.2.  Plane in space

  4.2.  Plane in space

Where   4.2.  Plane in space

If you know the general equation of the plane, then you can easily find the normal equation of the plane:

  4.2.  Plane in space

Where   4.2.  Plane in space   4.2.  Plane in space

The plus sign or minus sign is chosen so that p > 0. The angles α, β, γ are the angles between the normal vector n and the axes O x , O y , O z, respectively.

If the normal equation of the plane is known, then it is easy to find the distance ρ from the point   4.2.  Plane in space to this plane:

  4.2.  Plane in space


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Linear Algebra and Analytical Geometry

Terms: Linear Algebra and Analytical Geometry