Questions about pararell planes in R3.

Hi!

I got two parallel planes in R3 given by the equations 3x + 4y -5z = 0 & 3x + 4y - 5z = 20. I have plotted them with

z1 = @(x,y) 0.6*x + 0.8*y;
z2 = @(x,y) 0.6x + 0.8*y -4;
fsurf(z1);
hold on
fsurf(z2);

I would like to find the normal vector by using matlab, I know its [3 4 -5] from the equations but I'd like to know how I cand find it using matlab.

Then I would like to plot the normal vectors between the planes, and measure the distance between the planes. So my questions are;

How do I find a normal vector to a plane in Matlab?

How do I plot it between the two planes?

And how do I measure the distance?

Best regards

[Aitor]

Did you ever get an answer?

If you did, can you tell me how to do it please.