Is there a way to get the result of a cross product to be normalized after just a cross action, i.e. without doing after the cross v/|v|
? (the vectors involved are not normalized, but they are orthogonal).
normalized cross product
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vector-analysis
cross-product
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0One can actually set things up so that you can (iteratively) compute $\sqrt{x^2+y^2}$ (probably) more cheaply than squaring $x$ and $y$ and rooting their sum. If you're interested in that, you can ask a separate question and I'll be happy to elaborate. – 2011-05-04
1 Answers
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If two vectors are orthogonal, then the length of their cross product is the product of their lengths. So if by "normalized" you mean length $1$, just divide by the product of the lengths of the two vectors.
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0@Emre: If he already thinks square roots are expensive, then certainly trigonometric functions would $b$e even more costly to evaluate. – 2011-05-04