Question

The points (0,0,0) (1,0,1) (1,1,0) and (0,1,1) are the vertices of a regular tetrahedron.

a)show that all six edges have equal length
b)find the angle between any two edges

Answer 1

It's been awhile since I have done this. Is there a faster way than calculating the length of all six vectors for a)?

Answer 2

and for b, is this correct?

\[\overrightarrow{AB}\cdot \overrightarrow{AC}=||\overrightarrow{AB}||\,||\ \overrightarrow{AC}||\cos{\theta}\]\[\cos{\theta}=\frac{\overrightarrow{AB}\cdot \overrightarrow{AC}}{||\overrightarrow{AB}||\,||\ \overrightarrow{AC}||}\]\[\cos{\theta}=\frac{1}{2}\]\[\theta=\frac{\pi}{3}\]