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Append a z-axis to the 2-dimensional plane and conquer the realm of 3-dimensional space.

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In the above regular octahedron \(ABCDEF,\) \(M\) and \(N\) are the midpoints of \(\overline{BC}\) and \(\overline{CD},\) respectively. If \(\theta\) is the angle between \(\overrightarrow{NF} \text{ and } \overrightarrow{MA}, \) what is the value of \(\cos \theta?\)

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Count the number of pairs of edges in the above cuboid that are skew.

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Find the distance between the following two lines:

\[\begin{cases} l_1: x=-y=8-z \\\\ l_2: x=y \text{ and } z=-10. \end{cases}\]

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