Equations of Lines and Planes: Examples

1. Find the Parametric and Symmetric equations of the line passing through the points (1,5,3) and (2,-4,1).

Anwser:

The anwser is pretty strait forward, so Maple isn't much help there. However, Maple is able to produce graphs of parametric equations. For this, we need to activate the plots package:

>	with(plots);

Then it is as follows:

>	spacecurve([1+t,5-9*t,3-2*t],t=-10..10);

2. Find the linear equation of a plane formed by the vectors <1,1,1> and <3,1,2> at the point (5,-3,2).

Anwser
First we must find the normal vector by taking the cross product of the two vectors

>	<1,1,1> &x <3,1,2>;

Then we find the equation by using the formlua:

>	1*(x-5)+1*(y+3)-2*(z-2)=0;

>	solve(x+2+y-2*z = 0,z);

>	plot3d(1/2*x+1+1/2*y,x=-10..10,y=-10..10);

>