Geometry Question

1. Apr 19, 2005

The Rev

Do lines have to be intersecting in order to be perpendicular?

For example, is a line which is perpendicular to a plane perpendicular to only the lines on that plane which intersect with it, or ALL lines on that plane?

Thanks.

$$\pi$$

The Rev

2. Apr 19, 2005

dextercioby

No,of course not,once u consider euclidean geometry in 3 dimensions.I think u gave the answer yourself.A line perpendicular to a plane is perpendicular on any line from that plane.And obviously the 2 lines are not coplanar & don't intersect...

Daniel.

3. Apr 20, 2005

Hurkyl

Staff Emeritus
Like being parallel, there isn't really a standard way of defining perpendicular lines in 3-space. Some prefer them to be intersecting, others not.

4. Apr 20, 2005

snoble

Maybe it's just me but I always thought of perpendicular as being a term that applies to vectors not lines. So a plane is perpendicular to a vector x if all the vectors in the plane (not lines) were perpendicular the the vector x. Since vectors intersect at the origin there's no real confusion.

I guess it should be easy to extend this definition of lines just by saying two lines are perpendicular if their direction vectors are perpendicular. Or you could require intersection. I guess it depends on the source you are working with.