Pre-calculus Contents J
 
 
Points, Lines and Planes in Three-dimensional Coordinate System Represented by Vectors
     Line in a three-dimensional (3D) coordinate system
      Equations of a line in space
         The vector equation of a line
         The parametric equations of a line
         Equation of a line defined by direction vector and a point - Symmetric equation of a line
         Line given by two points
         Distance between two given points
      Orthogonal projection of a line in space onto the xy coordinate plane
         A line in a 3D space examples
         Angle between lines
      Condition for intersection of two lines in a 3D space
     Plane in a three-dimensional (3D) coordinate system
      Equations of a plane in a coordinate space
         The equation of a plane in a 3D coordinate system
         The Hessian normal form of the equation of a plane
         The intercept form of the equation of a plane
         A plane in a 3D coordinate system examples
         Equation of the plane through three points example
      The distance between a point and a plane - plane given in Hessian normal form
         Comparison of the general form and the Hessian normal form of equations of a plane
      The distance of a point to a plane - plane given in general form
         Angle (dihedral angle) between two planes
     Line and Plane
      The line of intersection of two planes
         Projection of a line onto coordinate planes
      How determine two planes of which, a given line is their intersection line
      Intersection point of a line and a plane
      Sheaf or pencil of planes
         Points, Lines and planes relations in 3D space examples
      The angle between line and plane
     Point, Line and Plane - orthogonal projections, distances, perpendicularity of line and plane
      Through a given point pass a line perpendicular to a given plane
      Given a line and a point, through the point lay a plane perpendicular to the line
      Projection of a point onto a plane
      Projection of a point onto a line
         Through a given point pass a line perpendicular to a given line example
         Projection of a line onto a plane example
         Plane laid through a given point, such that be parallel with two skew lines example
         Plane laid through a given point, such that be parallel with two parallel lines example
         Distance between point and line example
         Distance between point and plane example
         Distance between parallel lines example
         Distance between two skew lines example
Pre-calculus Contents
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