Let `k` be the length of any edge of a regular tetrahedron (a tetrahedron whose edges are equal in length is called a regular tetrahedron). Show that the angel between any edge and a face not containing the edge is`cos^(-1)(1//sqrt(3))` .

Explanation

To show that the angle between any edge and a face not containing the edge of a regular tetrahedron is \( \cos^{-1}\left(\frac{1}{\sqrt{3}}\right) \), we can follow these steps:

### Step 1: Define the Tetrahedron and Vectors
Let the vertices of the regular tetrahedron be \( A, B, C, \) and \( O \). The length of each edge is \( k \). We can represent the vectors corresponding to the edges as:
- \( \vec{OA} = \vec{a} \)
- \( \vec{OB} = \vec{b} \)
- \( \vec{OC} = \vec{c} \)

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