The intersection of two planes is a line. If the planes do not intersect, they are parallel. They cannot intersect at only one point because planes are infinite.

## Where do planes intersect?

Plane-Plane Intersection

• Two planes always intersect in a line as long as they are not parallel.
• To uniquely specify the line, it is necessary to also find a particular point on it.

## Can planes intersect in geometry?

Summary. There are three possible relationships between two planes in a three-dimensional space; they can be parallel, identical, or they can be intersecting. If the normal vectors are not parallel, then the two planes meet and make a line of intersection, which is the set of points that are on both planes.

## In what ways can 2 planes intersect?

Two planes (in 3 dimensional space) can intersect in one of 3 ways:

• Not at all – if they are parallel.
• In a line.
• In a plane – if they are coincident.

## Where do planes and lines intersect?

In analytic geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or a line. It is the entire line if that line is embedded in the plane, and is the empty set if the line is parallel to the plane but outside it.

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## What is the intersection of two planes answer?

Answer and Explanation: The intersection of two planes is called a line.

## Do 2 planes always intersect?

Intersecting planes are planes that are not parallel, and they always intersect in a line. The two planes cannot intersect at more than one line. The above figure shows the two planes, P and Q intersect in a single line XY.

## What is a intersection of plane in geometry?

Intersecting planes are planes that intersect along a line. Planes p and q intersect along line m. Planes p and q do not intersect along a line. They are parallel.

## When two lines intersect their intersection is A?

A line contains at least two points. If two lines intersect, then their intersection is exactly one point.

## Can two planes intersect at a ray or a segment?

They cannot intersect at only one point because planes are infinite. Furthermore, they cannot intersect over more than one line because planes are flat.

## Where do two lines cross?

When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share a common point, which exists on all the intersecting lines, and is called the point of intersection. Here, lines P and Q intersect at point O, which is the point of intersection.

## Can a line and a plane intersect at exactly two points?

The statement ” a line can never intersect a plane at exactly two points ” is either an axiom in some formalization of Euclidean geometry or follows so directly from one or two other axioms in the system that the answer seems empty of meaning, a restatement of definitions (as in some of the good answers here).