Re: Are points co-planar in (numDimensions-1)?
- To: mathgroup at smc.vnet.net
- Subject: [mg43344] Re: Are points co-planar in (numDimensions-1)?
- From: "Kevin J. McCann" <kjm at KevinMcCann.com>
- Date: Tue, 26 Aug 2003 07:13:16 -0400 (EDT)
- References: <bi195e$akp$1@smc.vnet.net> <bi7nu3$pc8$1@smc.vnet.net> <bia0al$cr7$1@smc.vnet.net> <bich28$21u$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
If the formula holds with k1,k2,k3 not all zero, then the three vectors (from the origin to each point) are linearly dependent. Since any two non-collinear vectors define a plane, and the third is a linear combination of these two, the three vectors are coplanar. The statement is true in either direction. Kevin "AngleWyrm" <no_spam_anglewyrm at hotmail.com> wrote in message news:bich28$21u$1 at smc.vnet.net... > "AngleWyrm" <no_spam_anglewyrm at hotmail.com> wrote in message news:bia0al$cr7$1 at smc.vnet.net... > > > > Thus, to summarize, if a,b, and c are coplanar (and not 0), then there exists some relation of the > > form: > > k1 a + k2 b + k3 c = 0 > > Which brings up a good point about logic: > IF [points are coplanar] THEN [formula holds] > does not necessarily mean: > IF [formula holds] THEN [points are coplanar] > > Does anyone know how to test this situation? >