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

  • Thread starter The Rev
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In summary, the definition of perpendicular lines can vary depending on the context. In 3-dimensional Euclidean geometry, a line perpendicular to a plane is perpendicular to all lines in that plane, not just the ones that intersect with it. However, in some cases, perpendicularity may be defined by the intersection of two lines or the perpendicularity of their direction vectors. It ultimately depends on the source and context of the problem.
  • #1
The Rev
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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.

[tex]\pi[/tex]

The Rev
 
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  • #2
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
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
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.
 

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

What is Geometry?

Geometry is a branch of mathematics that deals with the study of size, shape, relative position of figures, and the properties of space.

What are the basic elements of Geometry?

The basic elements of geometry include points, lines, angles, planes, and shapes such as circles, triangles, and squares.

What is the difference between 2D and 3D Geometry?

2D geometry deals with objects or shapes that have only two dimensions - length and width. 3D geometry, on the other hand, involves objects or shapes that have three dimensions - length, width, and height.

How is Geometry used in real life?

Geometry is used in various fields such as architecture, engineering, art, and navigation. It helps in designing buildings, bridges, and roads, creating computer graphics, and determining the location of objects.

What are the different types of angles in Geometry?

There are four types of angles in geometry - acute, right, obtuse, and straight. Acute angles are less than 90 degrees, right angles are exactly 90 degrees, obtuse angles are greater than 90 degrees but less than 180 degrees, and straight angles are exactly 180 degrees.

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