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 Tumbleweed
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  • 9 votes cast
Jan
29
accepted Closed-form solution to 3D vector rotation problem
Jan
27
comment Closed-form solution to 3D vector rotation problem
Thanks, I added a recap panel and edited the picture. The z axis is still flipped, mainly because showing angles arcs greater than $\frac{\pi}{2}$ makes the drawing very cluttered and confusing. However, that should only make a difference when determining the signs of the rotation elements, conceptually it should not have any importance for understanding the problem
Jan
27
revised Closed-form solution to 3D vector rotation problem
fixed image
Jan
27
revised Closed-form solution to 3D vector rotation problem
added summary of problem properties
Jan
26
asked Closed-form solution to 3D vector rotation problem
Jan
26
answered Closed-form solution to 3D vector rotation problem
Nov
3
awarded  Tumbleweed
Oct
27
awarded  Teacher
Oct
27
answered Find the closed form of $\tan\frac{\pi }{64}$ by using the number $2$ only?
Oct
11
revised Local maxima when multiplying two functions
added 39 characters in body
Oct
11
comment Local maxima when multiplying two functions
I see, yes that makes sense. So that question is, when do we find a "bump" in the product?
Oct
11
awarded  Commentator
Oct
11
comment Local maxima when multiplying two functions
sorry what do you mean by f|g?
Oct
11
revised Local maxima when multiplying two functions
restated the question more explicitly
Oct
11
comment Local maxima when multiplying two functions
sure, I'll try, let me know if I can clarify further - I'm still trying to formalise it properly in my head!
Oct
11
comment Local maxima when multiplying two functions
ok so this is definitely one right answer, but I don't think it covers all the possibilities. If for example $g(x)$ is a monotonically increasing/decreasing function in the neighbourhood of 0, then $f(0)g(0)$ should still give a local maximum, right?
Oct
11
asked Local maxima when multiplying two functions
Sep
27
awarded  Curious
Sep
26
accepted Proving maximum of dot product using derivatives
Sep
26
comment Proving maximum of dot product using derivatives
This is a really cool argument, thank you very much. In the same way I guess one could prove that for $a \cdot b$ to have a minimum, then $a′$ and $b$ must be parallel. It is a bit cyclical maybe since you need the notion that $a′ \cdot b$=0 for perpendicular vectors here, and $a′ \cdot b$=1 in the parallel case, but I really like the reasoning. One question though, why did you say in the beginning that the dot product is non-zero for non-zero b? Wouldn't it be zero for perpendicular vectors?