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 14h comment Abbreviated notation for “vector normalized by its length” (unit vector) Great, but if you do use vector notation then $$\hat{\vec{x}}$$ is rather ugly. I have seen $$\langle \vec{x} \rangle$$ sometimes though. 14h revised How to understand rotation around a point VS rotation of axes? added 12 characters in body Apr 24 comment calculate arbitrary points from a plane equation From the information I in this answer use the two direction vectors to form a rectangle. Apr 24 revised calculate arbitrary points from a plane equation added 94 characters in body Apr 24 revised calculate arbitrary points from a plane equation added 787 characters in body Apr 24 revised calculate arbitrary points from a plane equation added 787 characters in body Apr 24 revised calculate arbitrary points from a plane equation added 787 characters in body Apr 23 comment Volume from equation $(x ^2+ y ^2 + z ^2 ) ^2 = xyz$ Yes, I fixed it. In spherical coordinates the distance is implicitly considered always positive and thus the absolute value in the expression for $r$. Apr 23 revised Volume from equation $(x ^2+ y ^2 + z ^2 ) ^2 = xyz$ added 2 characters in body Apr 23 comment calculate arbitrary points from a plane equation Possible duplicate of How do I get three non-colinear points on a plane? Apr 23 comment calculate arbitrary points from a plane equation Possible related question/answer on SO (stackoverflow.com/a/23474396/380384) Apr 23 answered calculate arbitrary points from a plane equation Apr 23 answered Volume from equation $(x ^2+ y ^2 + z ^2 ) ^2 = xyz$ Apr 17 comment Tangent parallel to the initial line for polar equation =, can r^2 be used instead? You mean minimum right? And only with the form $y=\sqrt{1+x^2}$ the minimum is the same as $y^2=1+x^2$. Apr 17 revised Tangent parallel to the initial line for polar equation =, can r^2 be used instead? deleted 37 characters in body Apr 17 answered Vector representation Apr 16 comment Use least squares to find best fit value of angle phi $s$ is a scale in order to make the $M$ matrix orthonormal ($M^\top M = \mathtt{1}$) and thus like a rotation matrix. By pulling the skew symmetric part out of $A$ we have almost a rotation, except for the scaling factor $1+s$. Again we want to minimize $s$, or at least be happy it is small value. Apr 14 revised What is the value of $\tan (\frac{\pi}{2} - \epsilon)$? added 38 characters in body Apr 14 comment What is the value of $\tan (\frac{\pi}{2} - \epsilon)$? Thanks. I'll keep it in mind. Apr 14 comment What is the value of $\tan (\frac{\pi}{2} - \epsilon)$? Cause I am an engineer and not a mathematician. To me it is an approximation.