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