Talk:Perpendicular

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The lede to this article previously said:

A line is said to be perpendicular to a plane if 1) the line intersects the plane, 2) the line is not completely contained in the plane, and 3) the line is perpendicular to some line in the plane.

But this is wrong. Any line that intersects a plane is perpendicular to some line in the plane. The correct definition is that a line is perpendicular to a plane if it is perpendicular to every line in the plane. I've changed this definition. —Bkell (talk) 19:16, 25 August 2013 (UTC)Reply

Er, well, a line is perpendicular to a plane if it is perpendicular to every line in the plane that it intersects. I guess the line won't intersect every line in the plane. —Bkell (talk) 19:22, 25 August 2013 (UTC)Reply

What is the foot of the perpendicular if it is not at the bottom as in the diagram? I think I know but it could be made explicit. — Preceding unsigned comment added by 86.145.80.46 (talk) 09:09, 20 July 2017 (UTC)Reply

Yes, you think correctly, draw an oblique line and construct a vertical line on it ... dare it, make an instance image of it and put it under "Foot of a perpendicular".--Petrus3743 (talk) 12:58, 20 July 2017 (UTC)Reply

I have just added a verbal description of this term in the section titled "Foot of a perpendicular" so that the definition is not just in a caption. --Bill Cherowitzo (talk) 17:38, 20 July 2017 (UTC)Reply

I am thinking of something along these lines:

${\displaystyle {\vec {r}}_{1}=x_{1}{\hat {x}}+y_{1}{\hat {y}}=x_{1}{\hat {x}}+m_{1}x_{1}{\hat {y}}}$

${\displaystyle {\vec {r}}_{2}=x_{2}{\hat {x}}+y_{2}{\hat {y}}=x_{2}{\hat {x}}+m_{2}x_{2}{\hat {y}}}$

${\displaystyle {\vec {r}}_{1}\cdot {\vec {r}}_{2}=x_{1}\cdot x_{2}\left(1+m_{1}m_{2})\right)=0}$

${\displaystyle m_{1}m_{2}=0}$

Guy vandegrift (talk) 23:22, 28 January 2024 (UTC)Reply

I think the notation might be a bit confusing for the plausible audience for this article (e.g. high school students) without further elaboration and a picture, and could probably be clearer even for an advanced audience; I'd avoid using products xx and yy with differing decorations in favor of using distinct letters.

Ideally this article should be more substantially expanded with a proper explanation of what the dot product is and why a dot product of zero means two vectors are perpendicular, written in as gentle a way as possible. –jacobolus (t) 00:54, 29 January 2024 (UTC)Reply

Forgive a newbie, but shouldn't the ninety degree angles have square "markers"? 213.89.13.125 (talk) 18:05, 30 June 2024 (UTC)Reply

There seem to be three related subjects here:

• the adjective perpendicular (?title, introduction, current short description)
• the concept of perpendicularity (treated along with the adjective)
• the noun perpendicular, meaning a line perpendicular to something (first section after the introduction).

At present there's a feeling of the article switching between them, rather than taking one as the main subject and treating it as the context for the others.

Part of the confusion comes from the article title being the adjective, I think—assuming it's not meant to be about perpendiculars.

I wonder if it should be moved to Perpendicularity or something like Perpendicular (concept). Or at least, judiciously edited to put everything in the context of one main meaning.

(I ended up commenting because I wanted to simplify the short description, then didn't know which of the three meanings to choose.) Musiconeologist (talk) 23:37, 9 January 2025 (UTC)Reply

I've now added a brief explanation of a perpendicular. I think it would also be useful to create a Terminology section, with very brief explanations (not rigorous definitions: those can be in other sections and linked to). Probably it should at least include (not necessarily in these words):

• two objects that meet at right angles are perpendicular, as described [above];
• a perpendicular is a line which is perpendicular to another object;
• dropping a perpendicular from a given point to a given line means constructing a perpendicular to the line so as to pass through the point;
• the point where the dropped perpendicular meets the line is called its foot.

People wanting a quick explanation could then find it by going straight to Terminology, and those wanting more mathematical detail could follow links to later sections. Musiconeologist (talk) 03:02, 10 January 2025 (UTC)Reply