Straight Line in Space
Point-Direction Form of the Equation of a Line
\[\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}\]
where the point P1(x1, y1, z1) lies on the straight line and the vector s (a, b, c) is direction vector of the line.
Two-Point Form of the Equation of a Line
\[\frac{x - x_1}{x_2 - x_1} = \frac{y - y_1}{y_2 - y_1} = \frac{z - z_1}{z_2 - z_1}\]
Equation of a Straight Line in Parametric Form
\[\left\{
\begin{aligned}
x &= {x_1} + t\cos\alpha \\
y &= {y_1} + t\cos\beta \\
z &= {z_1} + t\cos\gamma
\end{aligned}
\right.\]
where the point P1(x1, y1, z1) lies on the line and cos α, cos β, cos γ are the direction cosines of the direction vector of the line, the parameter t is any real number.
