\(2\) Dimensions

There are three cases to consider with respect to the way two lines may intersect in \( \mathbb{R}^2 \) .

1. Intersect in exactly one point

2. No intersection points - the lines
are parallel and distinct

3. Infinite number of intersection
points - the lines are coincident

\(3\) Dimensions

The three cases in which two lines may intersect in \( \mathbb{R}^2\) also exist in \( \mathbb{R}^3\). The two lines may

• intersect in exactly one point,
• be parallel and distinct and not intersect, or
• be coincident and intersect in an infinite number of points.

However, there is one additional possibility in \( \mathbb{R}^3 \) not found in \( \mathbb{R}^2 \): skew lines.