Should not angle between vector P and Q be 180-θ rather than θ? According to my book it is θ.
If you put them tail to tail you can see that the angle is theta. Actually OB is the vector Q translated so that it has same origin as P.
Another way to look at it is that the projection of Q along P is in the positive direction so the angle should be less than 90 degrees.
All this assumes that the vector Q is from A to C. It does not have an arrow in the drawing.
The parallelogram is just a 'construction'. The vectors are OA and OB, which makes the angle between them θ. Another way of looking at it is to consider the difference between the respective angles of each vector and the X axis (or any other axis).
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