Dumb math question: calculating angles from 3D coordinates

[Quinn]

This is something I should remember from high school geometry, but I don't. I have the following 3D model of a hexahedron:


http://www.jqpaxton.com/coordinates.jpg


I need to figure out the dimensions of it -- the lengths of all the edges and the angles of all the corners. The edge lengths I can do, but calculating the corner angles has got me stumped. Anyone who can point me toward some formulas and an example or two will receive my eternal gratitude.

[Fredrik]

Use this formula:

\vec{u}\cdot\vec{v} = |\vec{u}||\vec{v}| \cos \theta

There should also be a vector u on the left hand side. I typed it in and I don't see anything wrong with the LaTeX code. I don't know why it isn't displayed.

For example you get one of the angles by using the formula with the vectors (-13,0,0)-(-10,-3,0)=(-3,3,0) and (-7,0,3)-(-10,-3,0)=(3,3,3).

[Yllanes]

Use this formula:

\vec{u}\cdot\vec{v} = |\vec{u}||\vec{v}| \cos \theta

I typed it in and I don't see anything wrong with the LaTeX code. I don't know why it isn't displayed.


This forum's LaTeX support is very complete and is not limited to mathematical formulas. You need to include the math delimiters $...$, \[...\], etc. or it won't work. So your formula should be

$\vec{u}\cdot\vec{v} = |\vec{u}||\vec{v}| \cos \theta$

which gives

$ \vec{u}\cdot\vec{v} = |\vec{u}||\vec{v}| \cos \theta$