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 |
|---|---|
| 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.”