# Is the intersection of 3 planes always a line?

## Is the intersection of 3 planes always a line?

-a line (Three planes intersect in one unique line.) -no solution (Three planes intersect in three unique lines.) -a line (Two parallel/coincident planes and one non parallel plane.) -no solution (Two parallel/non-coincident planes and one non parallel plane intersect in two unique lines.)

### What are intersecting planes?

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.

#### Do 2 intersecting lines determine a plane?

Two intersecting lines determine a plane. If you hold two pencils so that they cross each other, there’s only one place a flat plane can be placed so that it rests on both pencils.

**How can three planes intersect at one point?**

three planes are parallel, but not coincident, all three planes form a cluster of planes intersecting in one common line (a sheaf), all three planes form a prism, the three planes intersect in a single point.

**When three planes intersect their intersection is always a plane True or false?**

12 Cards in this Set

One and only one distinct line can be drawn through two different points. | True |
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If a plane intersects two parallel planes, then the lines of intersection are parallel. | True |

If three random planes intersect (no two parallel and no three through the same line), then they divide space into six parts. | False |

## What is plane intersection postulate?

Plane Intersection Postulate – If 2 planes intersect, then they intersect at a line. Congruent – same size and shape.

### What determines a plane?

In a Euclidean space of any number of dimensions, a plane is uniquely determined by any of the following: Three non-collinear points (points not on a single line). A line and a point not on that line. Two distinct but intersecting lines. Two distinct but parallel lines.

#### Can three planes never intersect?

“Three planes can fail to have an intersection point, even if no planes are parallel.” This seems counter intuitive.

**Can 3 planes not intersect?**

“Three planes can fail to have an intersection point, even if no planes are parallel.”