Observe the schematic representation of the cloning vector pBR322...

Based on the schematic representation of the cloning vector pBR322, the restriction site for the enzyme $PvuI$ is located within the ampicillin resistance gene ($amp^{R}$).

When a foreign DNA fragment is successfully ligated at the $PvuI$ site, it disrupts the $amp^{R}$ gene. This phenomenon is known as insertional inactivation. As a result, the recombinant plasmid loses its ability to confer resistance to ampicillin.

However, the tetracycline resistance gene ($tet^{R}$) remains intact and functional because no insertion occurred within it. Therefore, the recombinant cells retain their resistance to tetracycline.

Consequently, the recombinant E. coli cells will be able to grow on a medium containing tetracycline but will fail to grow on a medium containing ampicillin.

Answer: They will grow on a medium containing tetracycline but fail to grow on a medium containing ampicillin.