Angle Between Vectors
Date: 06/07/2002 at 10:06:56 From: Rob Sears Subject: Angle between two vectors, clockwise direction about a normal vector with known direction I have two vectors in a plane, say A and B. I also have the normal vector to the plane made by A and B, say vector C (which obviously has an associated specific direction - being a vector). I know that the angle between the two vectors A and B can be evalulated using the dot product, Angle = acos((A.B)/(Mod(A)Mod(B))) but I need to know the clockwise angle from vector A to vector B when viewed in the direction of the normal vector C, not just the basic angle between A and B. I would appreciate your assistance. Best Regards Rob Sears
Date: 06/08/2002 at 11:10:45 From: Doctor Douglas Subject: Re: Angle between two vectors, clockwise direction about a normal vector with known direction Hi, Rob, Thanks for submitting your question to the Math Forum. Here's the algorithm: Since C points perpendicular to A and B, it points either parallel or antiparallel to the vector cross product A x B. If C points parallel to A x B, then the clockwise angle, when viewed ALONG the direction of C, is just the Angle that you calculated above. If C points antiparallel to A x B, then the clockwise angle is 360 deg - Angle. This assumes that you are using right-hand-rule conventions for the cross product. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/
Date: 06/10/2002 at 11:45:47 From: Rob Sears Subject: Thank you Doctor Douglas, Thanks very much for your response to this problem. Your assistance was very much appreciated. Please use this question on your website if you think that it would be of assistance to others. Best Regards, Rob Sears
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