We know that the plane passes through point A, and then we know its direction, so we can determine the plane. Because it involves the direction of the plane, we consider its normal, and it doesn't matter that A and B are intersecting straight lines. So the original problem is simplified as follows: We know that two intersecting straight lines A and B make an angle of 60, and we can find the straight line whose intersection makes an angle of 45 with A and B in space. The answer is four.
But I think there are only two such straight lines! The normal vector is considered in the "detailed explanation", and it can only be considered as "four" if different directions are counted. The plane in college physics also has a direction, but this is obviously not the answer to high school independent enrollment that does not involve this knowledge, so I also question the answer. Of course this is a good method, but my answer is two.
By the way, I am a self-enrolled candidate, taking the 20 12 exam.