Defining Lines as Parametric Equations 

Write the parametric equations for a line thru P=(1,2,3) parallel to the vector <3,4,5> 

Then define each parameter x(t), y(t), and z(t)  as a Maple function using the arrow (typed as the dash followed by the greater than sign ->) 

Use the spacecurve(...) function to plot lines defined as parametric equations. 

Place the cursor over the plot and experiment by changing the orientation of the graph so you can see the line 

Now let's look at planes. First we need to load the linalg library 

Find the equation of a plane through the 3 points A(0,0,1), B(2,0,0) and C(0,3,0) 

Find the normal vector to the plane by creating 2 vectors in the plane and taking their cross product 

Now we can form the equation of the plane as N · v where v is a vector on the plane 

So we could define v as <x-0, y-0, z-1> where we have chosen point A to be a point on the plane 

So our plane is 

which gives us the equation of the plane as the z variable, z = - x/2 - y/3 + 1 

Next we can use the implicitplot3d(...) command to plot the plane 

Rotate the plot so you can see the plane