Vectors – Understanding Vector Notation in Newtonian Mechanics

Question

I'm working with vectors and resolving them into their components on vector form, like this:
$$\vec{F} = F_1\hat{\imath}+F_2\hat{\jmath}.$$
I'm wondering whether we need to put vector notation over the components on the RHS, or whether we don't put vector notation on the components?

Answer 1

$F_1$ and $F_2$ are scalars, so should be left as you've shown them. $\hat{\imath}$ and $\hat{\jmath}$ are unit vectors. The 'hat' (^) symbol indicates both their vector nature and their unit magnitude, so no additional vector indication is needed.