The problem describes a person's movement: 4 km north, 3 km east, and 1 km down. To find the displacement, we can treat this as a 3D vector problem and apply the Pythagorean theorem in three dimensions.

The formula for displacement is: $\text{Displacement} = \sqrt{(x^2 + y^2 + z^2)}$ where:

• $x = 4 \, \text{km}$ (north)
• $y = 3 \, \text{km}$ (east)
• $z = 1 \, \text{km}$ (down)

$\text{Displacement} = \sqrt{(4^2 + 3^2 + 1^2)} = \sqrt{(16 + 9 + 1)} = \sqrt{26}$

Therefore, the displacement is $\sqrt{26} \, \text{km}$, corresponding to option B.