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Two intersecting straight lines uniquely define one single plane.

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Q: If to lines intersect how many planes contain both of the line?

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the parallel lines never intersect each other but they both intersect the line they are perpendicular to

Yes. But it does not mean it is fully. It partly is not. It is if both lines are in the same plane. But if they are in different planes, then they won't intersect.

In 3d space, two planes will always intersect at a line...unless of course they are the same plane (they coincide). Because planes are infinite in both directions, there is no end point (as in a ray or segment). So, your answer is neither, planes intersect at a line.

Algebra: If given two equations of a line, then you can assume that they are in the same plain. If the two slopes are equal, then the lines are parallel.Geometry: If given two lines in the same plane that never intersect, then these two lines are parallel. If the lines are in different planes, but never intersect, then the lines are skew.So, both definitions use lines and a plane. The answer is yes.

Since two parallel lines never intersect, they cannot be perpendicular to each other because perpendicular lines intersect and form angles of 90⁰.

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Think about it, the x & y planes intersect and what one number has both, the x & y planes intersect. 0 on the coordinate plane is the, origin.

none

true * * * * * No, false. Any two straight lines that intersect define a plane in which both those lines lie.

Two planes intersect at a line. The line where they intersect pertains to both planes. In the same manner, if infinitely many planes intersect each other at the same line, then that line pertains to the infinitely many planes.

the parallel lines never intersect each other but they both intersect the line they are perpendicular to

Yes. But it does not mean it is fully. It partly is not. It is if both lines are in the same plane. But if they are in different planes, then they won't intersect.

In 3d space, two planes will always intersect at a line...unless of course they are the same plane (they coincide). Because planes are infinite in both directions, there is no end point (as in a ray or segment). So, your answer is neither, planes intersect at a line.

No. Consider two adjacent faces on a cuboid. Both planes are parallel to the edge at which the intersect. But the fact that they do intersect illustrates that they are not parallel.

Algebra: If given two equations of a line, then you can assume that they are in the same plain. If the two slopes are equal, then the lines are parallel.Geometry: If given two lines in the same plane that never intersect, then these two lines are parallel. If the lines are in different planes, but never intersect, then the lines are skew.So, both definitions use lines and a plane. The answer is yes.

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.

Since two parallel lines never intersect, they cannot be perpendicular to each other because perpendicular lines intersect and form angles of 90⁰.

Lines that never intersect are either parallel or skew to each other. If they're both in the same plane (or on the same piece of paper), then they're parallel.