Need help finding the median of two directions

First post here, and sorry about the vague topic:

Im attempting to emulate a kingdom hearts style camera by keeping two objects in focus: the player and a target that's been locked onto. I just got into vector arithmetic, so Im having trouble wrapping my mind around this concept. But I will list a few points on my general idea:

1- When locked on, the camera follows the player, but focuses in the direction between the player and target, so as to keep them both in view.

2- (to be added later) when the target leaves the screen, the camera will whip around and place the target in the dead center of the screen.

Particularly on the first point, what would one do to find median of two directions? I would normally leave what Ive completed so far, but I'm just stumped. Any ideas?