The numerical ratio of displacement to the distance covered is always

$A$ person travels $10\, km$ north and $20\, km$ east. What will be the displacement from the initial point in $km$?

$A$ particle moves along the circumference of a circle of radius $r$ from point $A$ to point $B$ as shown in the figure. What are the path length and displacement?

The position of a body moving along the $x$-axis at time $t$ is given by $x = (t^2 - 4t + 6) \, m$. The distance travelled by the body in the time interval $t = 0$ to $t = 3 \, s$ is ...... $m$.

Explain frame of reference.

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?