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A tangent, but it (a) has nothing to do with croosing (whatever that may mean); and (b) while it does not cross the curve in the neighbourhood of the point of contact - there is no restriction on it crossing the curve at a distance.
It is a straight line.
It is the straight line joining the two points, A and B.
Y=mX+b
When a prod poss curve is a straight line, usually it is an exception, this means that as you produce more of one thing you constantly give up the same proportion of another thing as the scenario would be that the factors of production are 100% mobile. With a bowed out prod poss curve, usually called normal, the situation would be that as you produce more of product A you give up alot of B but eventually the rate of substitution begins to decline due to lack in factor efficiency and so the curve becomes less elasstic. Hope this answeres your question. all the best,