<p>In a regular tetrahedron, let θ be the angle between any edge and a face not containing the edge. The value of \(\cos^2 θ\) is</p>
Step-by-Step Solution
Key Concept: In a regular tetrahedron, the angle between an edge and the opposite face can be found using the geometry of the tetrahedron and the centroid of a face. The ratio GA/CA gives the sine of the angle to the normal, which relates to cos θ.
Let OABC be the regular tetrahedron. Let G be the centroid of the face OAB, then \(GA = \frac{1}{3}AC\). We have \(\cos θ = \frac{GA}{CA} = \frac{1}{3}\). Therefore, \(\cos^2 θ = \frac{1}{9} \times 3 = \frac{1}{3}\). ∴ Answer is (c) 1/3.
Correct Answer: C