Is power p a scalar or a vector? Why is there no direction? P = f / T, isn't f a vector? Is the dot product of two vectors scalar? Why?

Is power p a scalar or a vector? Why is there no direction? P = f / T, isn't f a vector? Is the dot product of two vectors scalar? Why?

We can't judge that P is a vector just because f is a vector
If P is a vector, do you say the direction of electric power is left or right?