Write the dimensional formula of power. Is power a vector or scalar quantity?

(N/A) Power $(P)$ is defined as the rate of doing work or the rate of transfer of energy. Mathematically,$P = \frac{W}{t}$.
The dimensional formula of work $(W)$ is $[ML^2T^{-2}]$.
The dimensional formula of time $(t)$ is $[T]$.
Therefore,the dimensional formula of power is:
$[P] = \frac{[ML^2T^{-2}]}{[T]} = [ML^2T^{-3}]$.
Power is a scalar quantity because it is defined as the dot product of force and velocity $(P = \vec{F} \cdot \vec{v})$,and it has only magnitude,not direction.