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Two planes that are not parallel intersect in a line.
If the two planes have normals m and n, their vector equations are m.r=c and n.r=d for c,d ∈ R. The angle α between the two planes is the same as the angle between their normals, and can be calculated using from m.n = |m||n|cosα.
The cross product of the normals m ×n gives a vector at right angles to both and therefore in the direction of the line of intersection of the planes.
Choosing a point a lying on the line of intersection, we can then write down the equation of this line:

r = a + tm ×n  where t ∈ R