which is not a possible type of intersection between three planes?
a) intersection at a point
b) three coincident planes
c) intersection along a line
d) intersection along a line segment
I know that planes can intersect in a line but I don't know which of c and d would be the correct answer
Please reread the question.
would it be d?
Looks good to me.
To determine the correct answer, you need to understand the concept of intersecting planes.
When two planes intersect, they can create three different possibilities for the intersection:
1. Intersection at a point: The two planes intersect at a single point.
2. Intersection along a line: The two planes intersect along a straight line. This line extends infinitely in both directions.
3. No intersection: The two planes do not intersect at any point. They are parallel or non-parallel planes.
Now, let's consider three planes and the possible types of intersections:
a) Intersection at a point: It is possible for three planes to intersect at a single point. This occurs when all three planes intersect at the same point.
b) Three coincident planes: This is not a possible type of intersection between three planes. Three planes cannot be coincident because, in three-dimensional space, three distinct planes cannot occupy the exact same position.
c) Intersection along a line: It is possible for three planes to intersect along a line. This occurs when all three planes intersect along the same straight line, meaning each plane intersects with the other two along the line.
d) Intersection along a line segment: This is not a possible type of intersection between three planes. A line segment is a finite portion of a line, and it cannot be formed by the intersection of three planes. The intersection of three planes would either form a line that extends infinitely in both directions or have no intersection at all.
Therefore, the correct answer is option d) intersection along a line segment.