I'm fairly new to vectors and using them in algebra, so please forgive me if this is a really basic question!
Say I have a point $P_2$ where $P_2 = P_1 + \vec{v}t$. I know $P_2$, $P_1$, $\vec{v}$. I know $P_2$ satisfies the equation due to prior calculations and want to solve for $t$. My confusion comes on the algebraic manipulation:
$P_2 = P_1 + \vec{v}t$ $P_2 - P_1 = \vec{v}t$ $\frac{P_2 - P_1}{\vec{v}} = t$
The last step is wrong, isn't it? One can't divide by a vector AFAIK. Then I thought, if I was to solve this just using an arbitrary element ($P_2-P_1$) divided by the corresponding element of $\vec{v}$, then I risk dividing by zero.
Is there a proper way to think about this and proceed with solving for t?