The intersection of two planes in three-dimensional space is a line, provided that the planes are not parallel or identical. When two planes intersect, they do so along an infinite set of points that forms a straight line.
To understand this concept better, imagine each plane as a flat sheet extending infinitely in all directions. When the two planes cut through each other, they create a line where the two flat sheets meet. If the planes are parallel, they do not intersect at all, and if they are identical, they coincide completely rather than intersecting in a single line.
Mathematically, this can be represented using equations for each plane. For instance, if a plane is defined by the equation Ax + By + Cz = D, the intersection can be found by solving the equations of the two planes together to find their common solutions, which will give us the equation of the line of intersection.
In summary, the intersection of two planes yields a line unless they are parallel or identical.