When (VECTOR) is the ACTive LEG, the
FMC does not automatically sequence to
the next wpt. It maintains heading
indefinitely. The next wpt becomes ACTive
only upon EXECution of the procedure for
proceeding direct to a wpt or intercepti ng a
leg to a wpt.
I interpret that as if you were to follow the missed approach vector, that vector would be active indefinitely.
Which is different to what OP is asking: how long the is the magenta line?