# Can you solve a system of three non-coplanar lines?

Feb 3, 2018

It depends what you mean...

#### Explanation:

If two lines intersect then they define a plane in which both lines lie. So those two lines are coplanar.

If three lines intersect in a common point, then any two of those lines are coplanar.

So what does it mean to say that three lines are "non-coplanar"?

It seems to me that it could mean one of two things:

(a) There is no plane containing all three lines.

(b) There is no plane containing more than one of the three lines.

In case (a) it is perfectly possible for all three lines to intersect in a common point. For example, the origin is the common intersection of the $x$-axis, $y$-axis and $z$-axis.

In case (b) no pair of lines intersect, so there is no common intersection point of all three lines.