Given below are equations for 2 planes in R3.
3x1 − 2x2 = 10
x1 + 2x2 + 4x3 = −2
Explain why these two planes must intersect in a line.
Their normals are <3,-2,0> and <1,2,4>
The only way that the two planes could not intersect is if they are parallel or plane equation is a multiple of the other.
Since their normals are not parallel, neither are the planes