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This is an archived, read-only copy of the United-TI subforum , including posts and topic from May 2003 to April 2012. If you would like to discuss any of the topics in this forum, you can visit Cemetech's Technology & Calculator Open Topic subforum. Some of these topics may also be directly-linked to active Cemetech topics. If you are a Cemetech member with a linked United-TI account, you can link United-TI topics here with your current Cemetech topics.

Math and Science => Technology & Calculator Open Topic
Author Message
WikiGuru
ADOS (Attention deficit... Oh! Shiny!)

Elite

Joined: 15 Sep 2005
Posts: 923

 Posted: 14 Jan 2009 01:25:09 pm    Post subject: When you take the dot product of two vectors both with units meters, is the resulting unit meters^2 or is it meters?
simplethinker
snjwffl

Active Member

Joined: 25 Jul 2006
Posts: 700

 Posted: 14 Jan 2009 01:37:32 pm    Post subject: It would be m2 A.B (let's pretend that little "." is bigger and centered vertically ) = |A||B|cos(θ) where θ=angle between them. Now, cos(θ) is a dimensionless quantity and both |A| and |B| have dimensions m, so the dimensions are m2
WikiGuru
ADOS (Attention deficit... Oh! Shiny!)

Elite

Joined: 15 Sep 2005
Posts: 923

 Posted: 14 Jan 2009 02:24:52 pm    Post subject: Oh, duh. That's how work is computed (Nm). Haha, brain fart. edit: Second question: What is the meaning of dotting two vectors with units meters? I know that the dot product determines the tendency of two vectors to point in the same direction, but with m2 units, it doesn't really make sense.Last edited by Guest on 14 Jan 2009 02:34:43 pm; edited 1 time in total
Galandros

Active Member

Joined: 29 Aug 2008
Posts: 565

 Posted: 14 Jan 2009 03:36:53 pm    Post subject: I though of that and I got nowhere. And I have to control my curiosity in class... In our class we give no unit.
simplethinker
snjwffl

Active Member

Joined: 25 Jul 2006
Posts: 700

 Posted: 14 Jan 2009 04:12:55 pm    Post subject: The dot product of two vectors with both units in meters (or any other unit) can be used as a scaling factor for certain situations (I can't think of a better way to phrase this). For example, if you had the vector r=(rx meters, ry) and you wanted to determine it's component in the direction of u=(ux, uy) meters (instead of in the directions (1, 0) or (0, 1)), doing r.u and dividing that by |u|2 (which is 1m2) gives the component in the direction of u (I think this is called the projection). This kind of thing appears frequently in Linear Algebra, fluid mechanics, optics and a bunch of other things (those were the first to come to mind).
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