What is meant by the parametric equations of a line in three-dimensional space?

Question

3373 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-08-20T19:28:30

We want to find the parametric equations of the line L passing through the point P and parallel to a vector A.

Let us take a 3-dimensional point in #R^3#, call it #P = (x_0,y_0,z_0)#.

A line L is drawn such that it passes through P and is parallel to the vector #A = (u,v,w)#.

3 parametric equations can be written which express the components:

#x = x_0 + tu#
#y = y_0 + tv# #(-oo < t < oo)#
#z = z_0 + tw#

As an example, with a point #P = (2,4,6)# and vector #A = (1,3,5)#, we have the following parametric equations:

#x = 2 + tu#
#y = 4 + 3v# #(-oo < t < oo)#
#z = 6 + 5w#