What are vertical columns and horizontal rows in the modern periodic table called? Mention how the following physical properties and give a reason in support of your answer in the above two cases.
a) Metallic character moving down a vertical column.
b) Atomic radius moving left to right in a horizontal row.

According to Mendeleev's periodic table, the vertical columns are called as groups and the horizontal rows are called periods.
The metallic character increases from moving down a vertical column. The atomic radius decreases from moving left to the right in a horizontal row.

Explanation:

The metallic character increases as we go down in a vertical column, and the atomic radius increases, which is easy for an atom to lose electrons because of the distance between the nucleus and the electron increases. The atomic radius decreases from moving left to the right as the outer shell electrons are in the same valence shell, and the effective nuclear charge increases, which causes more attraction of electron and nucleus, pulling them strongly to the nucleus.