Two parametric lines
An interactive 3D plot
See questions below.
This worksheet is intended to help you explore parametric lines in three-space.
The worksheet allows you to specify two points, \(P\) and \(Q\), two vectors v and w, and two parameters \(t\) and \(s\) (by default, \(t = 1\) and \(s = 1\)). Initially, four vectors will be plotted:
- v (in red) based at point \(P\),
- w (in green) based at point \(Q\),
- \(t\)v (in blue) based at point \(P\),
- \(s\)w (in blue) based at point \(Q\)
You should observe the effects of varying \(t\) and \(s\). If \(t\) is allowed to take on any real number value, the terminal points of \(\overrightarrow{p} + t\overrightarrow{v}\) describe a line. Note that you have the option of plotting the position vector \(\overrightarrow{p}\) corresponding to point \(P\) and the vector \(\overrightarrow{p} +t\overrightarrow{v}\). You also have the option of plotting the "entire line", but you'll need to zoom in to see the details if you do so.
So without further ado, click the “Evaluate” button below (the actual Sage code is included in the box only in case you're interested; you don't need to modify the code).