# Help in drawing planes in mathematica

1. Oct 11, 2009

### dg88

Hi,

I am trying to draw a plane that is normal to a given vector. I want to enter to the normal in polar coordinates so that I can manipulate the Theta and Phi and see how various planes cut the (111) planes in silicon crystal. Help would be much appreciated.

Cheers

2. Oct 11, 2009

### Hepth

Plane[\[Theta]_, \[Phi]_] = (-Cos[\[Phi]] Sin[\[Theta]] x -
Sin[\[Phi]] Sin[\[Theta]] y)/Cos[\[Theta]];
Plot3D[Plane[0.4, 0.2], {x, -1, 1}, {y, -1, 1},
AxesLabel -> Automatic, PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}},
BoxRatios -> {1, 1, 1}]

3. Oct 11, 2009

### dg88

Thanks a lot for your help. I went along with what you suggested and made some changes to go along. Here is the code that I did.

Manipulate[
Plot3D[z = (-Cos[\[Phi] Degree] Sin[\[Theta] Degree] x -
Sin[\[Phi] Degree] Sin[\[Theta] Degree] y +
r Sin[\[Theta] Degree] Cos[\[Phi] Degree])/
Cos[\[Theta] Degree], {x, -1, 1}, {y, -1, 1},
PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}}, BoxRatios -> {1, 1, 1},
Mesh -> None]], {{\[Theta], 0, "\[Theta]"}, 0, 180, 0.1,
Appearance -> "Labeled"},
{{\[Phi], 0, "\[Phi]"}, 0, 180, 0.1, Appearance -> "Labeled"},
{{r, 0.5, "R"}, 0, 1, 0.1, Appearance -> "Labeled"}]

Thanks again.

4. Oct 12, 2009

### dg88

I have a question if any one can answer this. I wrote down the equation for a plane in the post above. But what happens is that if I keep Theta = 0, any changes in Phi and R are not displayed, i.e., there is no effect if I change either one of them. But if I have a non-zero Theta, the changes in Phi and R are visible in the visual. This is odd. Is there anything that I am missing?? Thanks in advance.

Cheers

5. Oct 12, 2009

### Hepth

No, remember theta is the angle off of the upward Z axis, and phi is the angle ABOUT the Z axis. So if theta is zero, nothing should happen, because the vector is pointing up and revolving around itself, which is nothing.
R shouldn't change anything because a plane is defined by its normal unit vector, not the magnitude.