How can the resultant effect of motion be known?

Which among path length and displacement cannot be zero for a moving object?

"The magnitude of displacement may or may not be equal to the path length traversed by an object." Explain this statement with an example.

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 ...... $m$.

The position vector of a particle is given by the expression $\vec{r} = 3t^2 \hat{i} + 4t^2 \hat{j} + 7 \hat{k}$. The distance traversed in the first $10 \, s$ is ......... $m$.

On an open ground,a motorist follows a track that turns to his left by an angle of $60^{\circ}$ after every $500\; m$. Starting from a given turn,specify the displacement of the motorist at the third,sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.