<p>How many line segments have both their endpoints located at the vertices of a given cube.</p>
Step-by-Step Solution
Key Concept: Count all possible line segments between 8 vertices using combinations, which automatically includes edges, face diagonals, and space diagonals.
<p><strong>Solution:</strong> A cube has 8 vertices. Total line segments connecting any two vertices = \(\binom{8}{2} = 28\)</p><p>These 28 segments consist of:</p><p>1. Edges of the cube: 12</p><p>2. Face diagonals: 12 (2 diagonals per face × 6 faces)</p><p>3. Space diagonals: 4 (connecting opposite vertices)</p><p>Total = 12 + 12 + 4 = 28</p><p>∴ Answer is (B) 28</p>
Correct Answer: B