A line.
Unless the two planes are the same, in that case a plane.
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line
In three-dimensional space, two planes can either:* not intersect at all, * intersect in a line, * or they can be the same plane; in this case, the intersection is an entire plane.
Origin
In general no. The intersection of two parallel half-planes A and B is either a half-plane (either A or B, when A and B have similar orientation) or the empty set (when A and B have opposite orientation). When A and B are not parallel, their intersection is a maximal open region bounded by the two lines that define A and B, respectively. In this case, the intersection always exists and it is never a half-plane.
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