Practice Lines in 3D in Math

Quick Recap

Lines in three-dimensional space described using parametric equations $x=x_0+at$, $y=y_0+bt$, $z=z_0+ct$, or symmetric form $\frac{x-x_0}{a}=\frac{y-y_0}{b}=\frac{z-z_0}{c}$, where $(x_0,y_0,z_0)$ is a point on the line and $⟨a,b,c⟩$ is the direction vector.

In 2D, a line is defined by a slope and a point ($y=mx+b$). In 3D, slope doesn't work—there's no single number for direction in space. Instead, you specify a starting point and a direction vector (an arrow pointing along the line). The parameter $t$ acts like a slider: at $t=0$ you're at the starting point, and as $t$ increases or decreases, you slide along the line in the direction of the vector.