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:

$a x + b y + c z + d = 0$

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

$\left\{\begin{matrix}{a}_{1} x + {b}_{1} y + {c}_{1} z + {d}_{1} = 0 \\ {a}_{2} x + {b}_{2} y + {c}_{2} z + {d}_{2} = 0\end{matrix}\right.$

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