0
What else can I help you with?
What is intersection of two planes?
The intersection of two planes in three-dimensional space is typically a line, provided the planes are not parallel. If the planes are parallel, they do not intersect at all. If the two planes are coincident, they overlap completely, resulting in an infinite number of intersection points. The line of intersection can be found by solving the equations of the two planes simultaneously.
What is the maximum number of points of intersection when two circles and five straight lines intersect each other?
When two circles intersect, they can create a maximum of 2 intersection points. Each straight line can intersect with each of the two circles at a maximum of 2 points, contributing 10 points from the lines and circles. Additionally, the five straight lines can intersect each other, yielding a maximum of ( \binom{5}{2} = 10 ) intersection points. Therefore, the total maximum points of intersection are ( 2 + 10 + 10 = 22 ).
Can a plane and a line ever intersect in two points?
In Euclidean geometry, they can only intersect in 0, 1 or infinitely many points. If there are two points of intersection then the whole line lies in the plane.
What is the smallest number of points of intersection of five lines drawn in a plane?
The smallest number of points of intersection of five lines drawn in a plane occurs when all the lines are parallel. In this case, the lines do not intersect at all, resulting in zero points of intersection. Thus, the smallest number of points of intersection is 0.
What is the maximum number of points of intersection when two circles and five strait lines intersect ecah other?
32
How many different planes may share exactly one point?
None. In conventional geometry, any intersection of two planes defines a line, which is an infinite number of points. Many planes may intersect along a single line, or any pair of planes may intersect creating a unique line, but however they intersect, the number of shared points is infinite. If the the planes do not intersect (if they are parallel), then they share zero points.
Can two different planes intersect a line?
Yes, there are three ways that two different planes can intersect a line: 1) Both planes intersect each other, and their intersection forms the line in the system. This system's solution will be infinite and be the line. 2) Both planes intersect the line at two different points. This system is inconsistent, and there is no solution to this system. However, both planes will still be intersecting the same line, albeit at different locations on the line. 3) Both planes intersect each other, but their intersection does NOT form the line in the system. However, if the line in the system intersects the planes' intersection, then they will all intersect a single point. The solution will be finite and be a single point. There are also 3 ways two different planes WON'T both intersect a line. 1) The two planes and the line are all parallel to each other, and none of them intersect each other. 2) The line is parallel to one plane, but intersects the other plane. 3) The same as #2, but now the line is parallel to the other plane and intersects the one plane.
Do two planes intersect in infinitely many points?
No, perpendicular planes intercept at only one point. Parallel planes do not intersect at all.
Do planes intersect in exactly two points?
No. Either they do not intersect at all, or they intersect in a straight line or are the same.
What is the maximum number of points of intersection when two circles and five straight lines intersect each other?
When two circles intersect, they can create a maximum of 2 intersection points. Each straight line can intersect with each of the two circles at a maximum of 2 points, contributing 10 points from the lines and circles. Additionally, the five straight lines can intersect each other, yielding a maximum of ( \binom{5}{2} = 10 ) intersection points. Therefore, the total maximum points of intersection are ( 2 + 10 + 10 = 22 ).
What is the intersection of two distinct planes?
The intersection of two distinct planes is a line. The set of common points in the line lies in both planes.
Can 3 planes intersect at only 1 point?
No, they can intersect at infinitely many points.
Can two planes in three dimensional space intersect at one point?
No, the two planes intersect at a line, which is an infinite number of points.
Does intersection of 2 planes always contain at least 2 points?
YES. The intersection of two planes always makes a line. A line is at least two points.
Can two planes intersect in infinitely many points?
yes, it may be the two plane intersect at one line or the two planes are coincident.
What are the points where two or more segments intersect?
point of concurrency... or point of intersection
How many points of intersection do two skew lines have?
Any two lines can only have one point of intersection. Unless they are parallel, in which case they do not intersect at all. If they are the same line, then they intersect at an infinite number of points.
