Explanation:

- Consider the positions:

- P@Q: P is to the west of Q. Distance can be either 2 or 12 km.

- R&#Q: R is to the southeast of Q. Distance is not specified.

- Q$R: Q is north of R. Distance can be either 5 or 9 km.

- The arrangement suggests:

- If P is west of Q, and Q is north of R, R is southeast.

- The configuration forms a right-angled triangle with P and R as points on the hypotenuse, and PR is given as 13 km.

- Using the Pythagorean theorem for a right triangle:

- \( \text{QR}^2 + \text{PQ}^2 = \text{PR}^2 \)

- Possible PQ distances: 2 km or 12 km.

- Using \( QR + 2^2 = 13^2 \), QR is 12 km.

- Using \( QR + 12^2 = 13^2 \), QR is 5 km.

- Correct Option: 3. 5 km