Parametric Representations and Cartesian Equations of Lines
This page introduces the concept of représentation paramétrique d'une droite avec 2 points and provides the fundamental equations for representing lines in 3D space.
Definition: A parametric representation of a line is defined by a direction vector and a point on the line.
The parametric equations for a line are given as:
x = x_A + at
y = y_A + bt
z = z_A + ct
Where a,b,c is the direction vector and AxA,yA,zA is a point on the line.
Highlight: To determine a direction vector from a given parametric representation, look at the coefficients of the parameter t.
The page also introduces the concept of représentation paramétrique d'un plan, providing the equations for representing a plane parametrically.
Example: For a plane, the parametric equations are:
x = x_A + at + a't'
y = y_A + bt + b't'
z = z_A + ct + c't'
Where a,b,c and a′,b′,c′ are two non-collinear direction vectors, and AxA,yA,zA is a point on the plane.