Chapter 13 Section 13.5 Lines

x y z

A direction vector d for the line can be found by finding the vector from the first point to the second. To get a direction vector d that is perpendicular to both vectors u and v we can use the cross product.

This gives a system of equations with the variables t and u. Solve this system for t and u. This can be done in many ways here we equate the x and y components.

Symmetric Equation of a Line Beside the vector form of a line and the parametric form of a line, a line can also be expressed as three equivalent expressions of the x, y and z variables. This is done by solving the parametric system for t and equating them. In order to determine the direction vector d the coefficients of x, y and z all need to be 1. Divide the first expression by 3 and the second by -2.