The shortest distance between any two opposite edges of the tetrahedron is:
Step-by-Step Solution
Key Concept: The shortest distance between two skew lines equals the absolute value of the scalar triple product divided by the magnitude of the cross product of direction vectors.
From the given equations, $A(0,0,0)$ is a point on line (1) and $B(0,0,a)$ is a point on line (2). The shortest distance is $S.D = |[0-0) + m(0-0) + n(0-a)| = \left|-\frac{1}{\sqrt{6}}(-a)\right| = \frac{2}{\sqrt{6}}a$.
Correct Answer: 1