My Math Forum 2 unit vectors dot product

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 September 23rd, 2010, 05:05 AM #1 Newbie   Joined: Jul 2010 Posts: 26 Thanks: 0 2 unit vectors dot product I need certain stopping criterion for approximating one unit vector with another. In case there is a perfect match (after a number of iterations), the dot product of the vectors is 1. I need to know (and have a reasoning for) whether in any other case the dot product of the original unit vector and the approximation (which is also a unit vector) is less than 1. Thanks
 September 23rd, 2010, 08:07 AM #2 Senior Member   Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0 Re: 2 unit vectors dot product I presume that your vectors are in $\mathbb{R}^n$ for some n and the dot product is the usual one on this space. In that case, remember that the dot product is given by $|u||v|\cos\theta,$ where $\theta$ is the angle between u and v. In the case of two unit vectors, the dot product is just the cosine of the angle between them. What more, exactly, do you want to know?
 September 23rd, 2010, 08:48 AM #3 Newbie   Joined: Jul 2010 Posts: 26 Thanks: 0 Re: 2 unit vectors dot product That's all. I just need appropriate stopping criteria for the iterative procedure I implemented. Thanks

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