
Precalculus
Contents J 





Points,
Lines and Planes in Threedimensional Coordinate System Represented by
Vectors 


Line in a
threedimensional (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 threedimensional (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 









Precalculus Contents 



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