Three girls skating on a circular ice ground of radius $200 \; m$ start from a point $P$ on the edge of the ground and reach a point $Q$ diametrically opposite to $P$ following different paths as shown in the figure. What is the magnitude of the displacement vector for each? For which girl is this equal to the actual length of the path skated?

(B) Displacement is defined as the minimum distance between the initial and final positions of a particle.
In the given case,all three girls start from point $P$ and reach point $Q$.
Since $P$ and $Q$ are diametrically opposite points on a circular ground of radius $R = 200 \; m$,the displacement for each girl is equal to the diameter of the circle.
Magnitude of displacement $= 2 \times R = 2 \times 200 \; m = 400 \; m$.
Since the displacement is the shortest straight-line distance between two points,it is equal to the actual path length only when the path taken is a straight line.
Looking at the figure,girl $B$ follows a straight-line path from $P$ to $Q$.
Therefore,for girl $B$,the magnitude of the displacement is equal to the actual length of the path skated.