Any pair of perpendicular lines are coplanar?

Question

Any pair of perpendicular lines are coplanar?

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Answer 1

See the cube ABCD.EFGH (E is over A and F is over B)
AB and EH are perpendicular but not coplanar.

Answer 2

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 3

Let X be the point at the intersection of the lines.
Pick A and B on one line so that X lies between them.
Pick C and C on the other line so that X lies between them.
The sets of points {A, B, C} and {A, B, D} each define a plane.
Since X is on the line between A and B, X is in the plane defined by
{A, B, C} . Similarly X is in the plane as {A, B, D}

Since X is on a line connecting C and D, the line CD is in the same plane as the line from C to X and also the line from D to X, so they are the same plane. i.e. one plane that contains {A,B,C,D}.

Answer 4

As per dictionary.com, the definition of perpendicular would be
Mathematics. Intersecting at or forming right angles.
See: http://dictionary.reference.com/search?q=perpendicular

If we assume that the term "intersection" is vital, then they have to be coplanar. If however, that was not a necessity, then its not necessary to be coplanar

Answer 5

Yes you are true.

Any pair of intersecting lines form a plane so this inturn implies that intersecting lines are coplanar.

Two perpendicular lines are also intersecting lines but the angle of intersection is 90 degrees. So any pair of perpendicular lines are co-planar.

Any two non-skew lines are also coplanar.

Hope you can understand this.

Answer 6

Any pair of lines will always be coplanar.

Answer 7

True. Any pair of intersecting lines defines a plane.

Answer 8

given any two non skew lines, we can find a plane containing both the lines. so any two non skew lines are coplanar

Answer 9

true. A plane can befined as any pair of parralell lines.

Answer 10

perpendicular means that the 2 lines INTERSECT... (if they don't, you use the word "orthogonal")

and if they do, they DEFINE a plane.

so yes.