Leading the way to the Future
 14 Jan 2009 01:25:09 pm by WikiGuru When you take the dot product of two vectors both with units meters, is the resulting unit meters^2 or is it meters?
 14 Jan 2009 01:37:32 pm by simplethinker 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
 14 Jan 2009 02:24:52 pm by WikiGuru 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.
 14 Jan 2009 03:36:53 pm by Galandros I though of that and I got nowhere. And I have to control my curiosity in class... In our class we give no unit.
 14 Jan 2009 04:12:55 pm by simplethinker 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).