The Cartesian form of a vector line in 3D is obtained by eliminating the parameter λ from the parametric form.

Solving each equation for λ gives:

Equating these expressions yields the Cartesian form:

which clearly emphasizes the consistent ratio of coordinate changes along the line.

If one of the direction vector components is zero, then that coordinate does not change as you move along the line.

Example

Express the line

in vector form.