How to rearrange a scalar product equation to make a vector the subject? Mechanical work is defined as the scalar product of force (F) and displacement (s).
I.e. W = F.s
How can this equation be rearranged to make F or s the subject?
 A: Inherently, the problem as posed cannot be fully solved: say you know $W$ and $\mathbf{s}$, and that $W = \mathbf{F} \cdot \mathbf{s}$; then you do not have enough information to recover $\mathbf{F}$, since many different vectors $\mathbf{F}$ will give the same result.
You have gained some knowledge about $\mathbf{F}$ with $W = \mathbf{F} \cdot \mathbf{s}$, but not the full picture (unless you are in 1 dimension).
Let us consider a simple, 2D example: suppose that $W = 1$, and $\mathbf{s} = [1, 0]^{\top}$ (the transpose is just there so that it is a column vector, you can ignore it).
What this tells you, geometrically, is that the projection of $\mathbf{F}$ onto $\mathbf{s}$ is equal to 1, but infinitely many vectors satisfy this property: writing out the dot product explicitly, we have
$$
1 = W = 
\left[\begin{array}{c}
F_x \\ 
F_y
\end{array}\right]\cdot
\left[\begin{array}{c}
1 \\ 
0
\end{array}\right]
= F_x\,,
$$
which means that $F_x = 1$.
There is no constraint on $F_y$: any value for it will still satisfy the required property. So, any vector in the form $\mathbf{F} = [1, F_y]^\top$ will work.
This means that you cannot turn your equation into something of the form $\mathbf{F} = \dots$, since that would mean you have a unique solution to this problem, which does not exist.
You can also think of it like this: the equation $W = \mathbf{F} \cdot \mathbf{s}$ is a scalar equation, it relates numbers; while if you were to write $\mathbf{F} = \dots$ that would be a vector equation, which corresponds to several, independent scalar equations (as many as the dimension of your space, so often 3).
You cannot turn one equation into several, independent ones.
