Given velocity and position, when does it hit the plane? A particle at position $p$ and velocity $\vec{v}=\langle x,y,z \rangle$ hits the plane orthogonal to vector $\vec{n}$ and passing through point $q$. When does the particle hit the plane?
I calculated the distance between particle and plane, but my problem is how to convert vector into units so that I can calculate the time. I tried the magnitude, but it gives incorrect solution. Can someone point me in the right direction?

I think we're supposed to assume the particle travels at constant velocity $\bf v$, and at time $t = 0$ has position ${\bf r}\left(0\right) = \bf p$, so that it's position as a function of time is
$$
{\bf r}\left(t\right) = {\bf v} t + {\bf p}.
$$
This vector lies in the plane if
$$
\left[{\bf r}\left(t\right) - {\bf q}\right] \bullet {\bf n} = \left( {\bf v} \bullet {\bf n}\right) t + \left({\bf p} - {\bf q}\right) \bullet {\bf n} = 0 \Rightarrow t = \frac{\left({\bf p} - {\bf q}\right) \bullet {\bf n}}{{\bf v} \bullet {\bf n}}.
$$
