I have a couple arrow shapes pointing at a given angle as shown in the image below. I'd like to extend both arrow points together, further along the same trajectory. How can I do this maintaining the same relative positions of the arrow paths?
Since your arrows are shapes and not a path with a stroke and arrow head on it, you ill have to take the direct selection tool (white arrow) and select the 5 anchor points creating the arrow of each arrow [fist image from the left] and then drag them around or use the arrow keys to move them [second image].
Selecting an anchor point allows you to move only that point.
You might want to figure out the angle of your arrows, create a line at that exact angle and place it at the tip of one of the arrows to guide yourself along that line when moving them.
Bear in mind that once you select your individual anchors en masse with the direct select tool, when you first move them, if you start with one of the anchors on the arrow shaft, you can first move along the arrow shaft, and if you have Smart Guides on, once that vector has highlighted, you can hold down Shift to constrain your drag to that vector and you won't need to draw a manual guideline at the correct angle - Smart Guides handles that sort of task very well.