A vector line is defined by specifying one fixed point on the line and a direction vector. If the fixed point is given by position vector a, and the direction vector by b, then the line in vector form is:

Here, λ∈R is a parameter that varies over all real numbers, generating every point on the line. Changing λ moves the point r along the direction of b, creating the full infinite line.

Example

Find the equation of the line passing through ⎝⎛​101​⎠⎞​ parallel to ⎝⎛​−123​⎠⎞​.