Can two planes intersect in exactly one point?

2 Answers
Dec 14, 2016

As explained below.


Planes are not lines. Only lines intersect at a point. Planes intersect along a line.

Dec 16, 2016

See explanation...


There are several ways to think about this. Here's one...

The general equation of a plane in three dimensional (Euclidean) space can be written (non-uniquely) in the form:

#ax+by+cz+d = 0#

Given two planes, we have two linear equations in three variables:

#{ (a_1x+b_1y+c_1z + d_1 = 0), (a_2x+b_2y+c_2z + d_2 = 0) :}#

Either these equations will be inconsistent, or they will have an infinite number of solutions.