Trouble understanding notation of a given diagram

Question

In the following image, what does A and ΔA represent?

Answer 1

It's hard to know for sure without context, but it looks like $A$ is a position vector that changes over time, so $A(t)$ is the position at time $t$. Then you add a (probably small) amount of time to get to time $t + \Delta t$, which gives the new position vector $A(t + \Delta t)$. But since you can always add and subtract vectors from each other, we can say that $A(t + \Delta t) = A(t) + \Delta A$, in other words we define $\Delta A$ as the change in the vector between time $t$ and time $t + \Delta t$.

The other two vectors shown are then the components of $A(t + \Delta t)$ in parallel and perpendicular to the original vector $A(t)$.