A

Let the positions of the two points be represented by vectors. The distance between them is given as \( a \). Their relative velocity \( v \) has components \( u \) along the direction of \( a \) and \( \nu \) perpendicular to \( a \).

At the moment they are nearest, the relative position vector must be perpendicular to the relative velocity vector. Hence, we derive the condition for minimization. The minimum distance is derived from the Pythagorean theorem as follows:
\[ d = \sqrt{a^2 - (ut)^2}
\]
This leads to the first result regarding distance, which gives us the condition. Consequently, the time at which they are closest can be derived from \( t = \frac{a}{u} \), considering the initial components along the axis.

Thus, the conditions set forth in the problem statement confirm the results obtained.