I have a parameterized function of 3-d vectors defined as: $$ t(A\vec{u} - \vec{v}) = \vec{p} $$ Where $t$ is time, $\vec{u}$ is a variable vector, $A$ is a scalar constant, and $\vec{v}$ and $\vec{p}$ are vector constants.
I need to get this equation in terms of $t$, but there doesn't seem to be an obvious way to do this since it would involve division of vectors.
Once in terms of $t$, I must then find the vector $\vec{u}$ that minimizes $t$. I figure this part should be easy, as I can just take the derivative of the $t$ function with respect to $\vec{u}$ and set it equal to zero. However I first need to find the $t$ function, as mentioned above.