position vector
A position vector is the three numbers that say where a point sits relative to a frame's origin — typically written (x, y, z). Read them as a recipe for getting there from the origin: go x along the first axis, then y along the second, then z along the third, and you have arrived. That is all a position vector is: a set of step-by-step directions, in numbers, from the agreed starting corner to the spot you care about.
Calling it a 'vector' rather than just 'three numbers' is a reminder that it has both a direction and a length, and that it always rides on a particular frame. The point that is (0.3, 0.0, 0.5) metres in the camera frame might be (1.2, 0.4, 0.5) metres in the world frame — same physical point, different numbers, because the directions count from a different origin. So a position vector without a frame attached is like a street number with no street: you cannot find the door.
Position vectors are the raw material a robot reaches with. The arm controller is handed a target position vector for the gripper, the perception system outputs a position vector for each object it spots, and the navigation stack tracks the robot's own position vector on the map. Crucially, a position vector only captures where a point is, not which way it is turned — that rotational half of the story is orientation, and the two together make up a full pose.
A vision system reports a bolt at position vector (0.45, -0.10, 0.02) metres in the table frame: 45 cm out along the table's length, 10 cm to the near side, and 2 cm up off the surface — enough for the arm to know exactly where to reach.
Three numbers, one frame: exactly where the bolt is.
The three numbers are usually distances in metres, but the same idea works in any units, and in 2D problems you simply drop the third number.