Question

Consider a unit cube with one one corner at the origin what is the angle between any two diagonals?

Answer 1

Answer:

1.231 rad

Step-by-step explanation:

Suppose that the vertex opposite the origin is (a, a, a), therefore, the geometric vector A = (a, a, a) is a diagonal of the cube. There are two opposite vertices (0, a, 0) and (a, 0, a), with which B = (a, 0, a) - (a, 0, a) = (a, -a, a) is the diagonal that intersects the first diagonal.

Now, $\theta = arccos(\frac{A\bullet B}{\left\| A \right\| \left\| B \right\|}) = arccos(\frac{a^2}{3a^2}) = arccos(\frac{1}{3}) = 1.231 rad$