When is it necessary to use vectors?

Which two motions are considered to be combined for motion in a plane?

$A$ body moves $6\,m$ north,$8\,m$ east,and $10\,m$ vertically upwards. What is its resultant displacement from the initial position?

An ant is moving on a plane horizontal surface. The number of degrees of freedom of the ant will be .........

The position of a particle is given by $\vec{r} = 3.0 t \hat{i} - 2.0 t^{2} \hat{j} + 4.0 \hat{k} \; m$,where $t$ is in seconds and the coefficients have the proper units for $\vec{r}$ to be in metres.
$(a)$ Find the velocity $\vec{v}$ and acceleration $\vec{a}$ of the particle.
$(b)$ What is the magnitude and direction of velocity of the particle at $t = 2.0 \; s$?

The coordinates of a moving particle at any time $t$ are given by $x = \alpha t^3$ and $y = \beta t^3$. The speed of the particle at time $t$ is given by