**Representation of Numbers on a Number Line**

To answer the given questions, let's first understand how numbers are represented on a number line.

A number line is a straight line where each point represents a number. Numbers to the right of zero are positive, and numbers to the left of zero are negative.

The distance between two consecutive points on the number line is equal. This distance is usually taken as 1 unit.

**Representing Vasu's Position on the Number Line**

In the given question, Vasu represents root 4.5 on the number line PW. The length of TS is 1 unit. To understand Vasu's position on the number line, let's analyze the given representation.

The position of Vasu, root 4.5, is shown on the number line PW. The length of TS is 1 unit. This means that the distance between T and S is 1 unit.

Based on this information, we can determine the position of zero and the points where 5.2 lies on the number line.

**(i) Representing Zero on the Number Line**

To find the representation of zero on the number line, we need to determine the point that divides the line PW into two equal parts.

Since the distance between T and S is 1 unit, we can see that V is the midpoint of TS. Therefore, V represents zero on the number line.

**(ii) Determining the Points for 5.2 on the Number Line**

To find the points where 5.2 lies on the number line, we need to determine the distance between V and the point representing 5.2.

We know that the distance between T and S is 1 unit. Since V is the midpoint of TS, the distance between V and T (or V and S) is 0.5 units.

Now, to find the points for 5.2, we need to divide this distance into smaller parts. Each part represents one unit.

Since 0.5 units is half of 1 unit, we need to divide it into 5 equal parts. Each part represents 0.1 units.

Starting from V, we can count these equal parts to the right to locate the points representing 5.2. We count 5 parts, as 5 * 0.1 units = 0.5 units.

Therefore, the points where 5.2 lies on the number line are between V and the fifth part to the right of V.

**Conclusion**

In conclusion, the letter V represents zero on the number line PW. The points where 5.2 lies on this number line are between V and the fifth part to the right of V.