User talk:Rtgjr

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Hello, Rtgjr, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are some pages that you might find helpful:

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I hope you enjoy editing here and being a Wikipedian! Please sign your messages on discussion pages using four tildes (~~~~); this will automatically insert your username and the date. If you need help, check out Wikipedia:Questions, ask me on my talk page, or ask your question on this page and then place {{helpme}} before the question. Again, welcome! RJFJR (talk) 21:14, 26 December 2009 (UTC)[reply]

Plane (geometry)

Regarding your post to the maths Wiki-project. The article is correct. Think of the plane z = 1 in xyz-space. This plane passes through r₀ = (0,0,1) and contains the vectors v = (1,0,0) and w = (0,1,0). So r₀ + sv + tw = (0,0,1) + s(1,0,0) + t(0,1,0) = (s,t,1) which does indeed parametrise the plane z = 1. If we compute your expression, we have r₀ + s(v − r₀) + t(w − r₀) = (0,0,1) + s(1,0,−1) + t(0,1,−1) = (s,t,1 − s − t). This last expression does not parametrise the plane z = 1; for example, when s = t = 0 we have the point (1,1,−1), which is not a point on the plane z = 1. ~~ Dr Dec (Talk) ~~ 21:51, 26 December 2009 (UTC)[reply]

What his expression actually describes is a plane passing trough the points r0, v and w, whereas the original is a plane passing trough r0 and containing the directions v and w.--LutzL (talk) 16:25, 30 December 2009 (UTC)[reply]