Can two planes intersect in exactly one point?
2 Answers
Dec 14, 2016
As explained below.
Explanation:
Planes are not lines. Only lines intersect at a point. Planes intersect along a line.
Dec 16, 2016
See explanation...
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.
