A vector line in three-dimensional space can also be expressed in parametric form, showing explicitly the equations for the x, y, and z coordinates separately:

Here, (x0​,y0​,z0​) is a point on the line, (l,m,n) are the components of the direction vector, and the parameter λ controls your position along the line. Changing λ moves the point continuously along the direction of the vector, producing the full infinite line.

Example

Express the line r=⎝⎛​132​⎠⎞​+λ⎝⎛​−320​⎠⎞​ in parametric form.