Are Perpendicular lines are coplanar.?

Answer 1

Sometimes........

Answer 2

Define Coplanar Lines

Answer 3

Lines that intersect define a plane. But be careful of above: "Any pair of lines will always be coplanar." which is not true. Take a pencil hold it horizontally. Now take another one and touch the first pencil with it. No matter at what angle you touch it, you will find that you can place a book (plane) cover so that both pencils lie on the book. Now hold one perpendicular to the other. and stop touching the pencils, move them away from each other a bit in all three directions. You'll see that if they are not parallel and are not touching you cant get them to lie on the book smug. Means that if they are non intersecting they lie on the same plane only if they are not parallel. (PS: Sometimes you will have to extend the line to get it to intersect ---- but then straight lines don't end by defn)

Answer 4

Always. This is the original definition of perpendicular lines. The concept of perpendicular makes no sense if the lines are not in the same plane.

Wait: I should rather say that if two lines are perpendicular, then there exists a plane such that both lines are coplanar. This is more robust.

Answer 5

Maybe. Suppose two parallel planes, each having a single line, such that the projection of each line on the other plane generates a line perpendicular to the line already there. Would you call the non-coplanar lines perpendicular? If your definition of perpendicularity is that the lines should meet at a right angle, then they are not perpendicular because they do not meet at a right angle -- or, indeed, at any angle.

Answer 6

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RE:
Are Perpendicular lines are coplanar.?

Answer 7

Yes they are always coplanar. Think of two sticks that you are holding perpendicular to each other. If you were to take point on the stick and pick and pick another point and connect them with string, you'd find that they all lie on the same plane, including the original lines.

Answer 8

Yes, 3 points will define a plane. A line drawn perpendicular to another line forms 3 points and any point on these two lines will be in the same plane.

Answer 9

Perpendicular lines are both coplaner and noncplaner. Looking at a 2-dimension, graph, they lie on the same plane.

Looking at a 3 dimension model, the lines can intersect, but don't necessarily have to lie on the same plane.

Answer 10

2 intersecting lines (perpendicular or otherwise) are always on the same plane. however 3 or more lines may or may not be.

Answer 11

Yes, because they have to intersect, which means that they are on the same plane. Skew lines, which are noncoplanar, cannot be considered perpendicular.