Analytic Geometry – Plane 1

Sabtu, 06 Juni 2020

 

Plane 1

 

• Parametric From

      

    Where (x, y, z) are the coordinater of any unknown point on the line, the 

    point P(x₁, y₁, z₁) lies in the plane, the vectors (a₁, b₁, c₁) and (a₂, b₂, c₂) 

    are parallel to the plane.

 

Figure

 

• Dihedral Angle Between Two Plane

   If the plane are given by

   A₁x + B₁y + C₁z + D₁ = 0,

   A₂x + B₂y + C₂z + D₂ = 0,

   Then the dihedral angle between them is

    

 

Figure

 

 

• Parallel Plane

   The plane A₁x + B₁y + C₁z + D₁ = 0 and A₂x + B₂y + C₂z + D₂ = 0 are 

   parallel if

    

• Perpendicular Plane

   The plane A₁x + B₁y + C₁z + D₁ = 0 and A₂x + B₂y + C₂z + D₂ = 0 are 

   parallel if are perpendicular if A₁A₂ + B₁B₂ + C₁C₂ = 0.

 

• Equation of a Plane Through P(x₁, y₁, z₁) and Paralel To the Vectors 

          (a₁, b₁, c₁) and (a₁, b₁, c₁) (Figure)

     

 

• Equation of a Plane Through P₁(x₁, y₁, z₁) and P₂(x₂, y₂, z₂), and 

         Paralel To the Vectors (a, b, c)

    

 

Figure

 

 

• Distance From a Plane To a Plane

   The distance from the point P₁(x₁, y₁, z₁) to the plane 

   Ax + By + Cz + D₁ = 0 is

     

 

Figure

 

• Intersection of Two Plane

    If the plane A₁x + B₁y + C₁z + D₁ = 0 and A₂x + B₂y + C₂z + D₂ = 0 

    intersection straight line is given by

      

      

Sumber

Labels: Mathematician

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