Homework Help Forum: Vectors & Geometry

Posted by Beta plus on Thursday, October 29, 2009 at 12:54am.

Let A= Ai I + A2 J + A3 K and B= Bi I + B2 J + B3 K, prove that A.B = AiBi + A2B2 + A3B3

• Vectors & Geometry - drwls, Thursday, October 29, 2009 at 9:39am

  Multiply out the dot product factors. (Ai I + A2 J + A3 K).(Bi I + B2 J + B3 K). Cross product terms like AiI.B2J will be zero because the two unit vectors I and J are perpendicular. You will be left with only the sum of the products of components along the same axis, like AiBi.

  
  

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