When is an object said to be in motion?

The position vector of a moving particle at time $t$ is $r = 3 \hat{i} + 4t \hat{j} - t \hat{k}$. Its displacement during the time interval $t = 1 \ s$ to $t = 3 \ s$ is

Under what condition is the magnitude of distance covered by an object equal to its displacement?

Are motion and position relative or not?

"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 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 ......... $m$.