At $3\text{ pm}$ the minute hand of a wall clock, placed normally on the wall, points to the West. In which direction the hour hand will point at $9\text{ am}$?

Let's establish the standard alignment of a clock's hands first:
* At $3\text{ pm}$, the minute hand points towards $12$ (which is normally North) and the hour hand points towards $3$ (which is normally East).

According to the problem, the clock is rotated such that at $3\text{ pm}$, the minute hand (pointing at $12$) points to the West.
This means the standard position of $12$ on this clock corresponds to the West direction.

Now let's find the directions for the remaining positions based on this rotation:

* If $12$ is West, then moving $90^{\circ }$ clockwise: $3$ must point to North.
* Moving another $90^{\circ }$ clockwise: $6$ must point to East.
* Moving another $90^{\circ }$ clockwise: $9$ must point to South.

At $9\text{ am}$:

* The minute hand points to $12$ (West).
* The hour hand points to $9$.

Since the position of $9$ corresponds to the South direction, the hour hand will point to the South.