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Dot product confusion

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109940] Dot product confusion
  • From: "S. B. Gray" <stevebg at ROADRUNNER.COM>
  • Date: Tue, 25 May 2010 06:32:38 -0400 (EDT)
  • Reply-to: stevebg at ROADRUNNER.COM

Given

ptsa = {{x1, y1, z1}, {x2, y2, z2}, {x3, y3, z3}};

I  thought the following expressions would be identical:

{aa, bb, cc}.ptsa  (* expression 1 *)
ptsa.{aa, bb, cc}  (* expression 2 *)

but they are not. They evaluate respectively as:

{aa x1 + bb x2 + cc x3, aa y1 + bb y2 + cc y3,
aa z1 + bb z2 + cc z3}

{aa x1 + bb y1 + cc z1, aa x2 + bb y2 + cc z2,
  aa x3 + bb y3 + cc z3}

Since ptsa is itself three xyz coordinates, the expressions might be 
ambiguous, but I assumed the dot product would always commute. Should 
there be a warning?

The first result is the one I want.

Steve Gray


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