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Mathematics-Online problems:

Interactive Problem 126: Transformation of Coordinates

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Let $ P$ be the point with coordinates $ (\sqrt{6},-\sqrt{6},2)$ with respect to the Cartesian coordinate system spanned by the canonical unit vectors of $ \mathbb{R}^3$. Find the spherical and the cylindrical coordinates of $ P$. Which Cartesian coordinates does point $ P$ have, if we rotate the coordinate system about the $ x$-axis by $ \pi/3$.

Solution:
Spherical coordinates of $ P$: $ r=$,      $ \varphi=$$ \pi/$,      $ \vartheta=\pi/$
Cylindrical coordinates of $ P$: $ \rho=\big($ $ \big)^{1/2}$,     $ \varphi=$$ \pi/$,     $ z=$
Cartesian coordinates after rotation (Results should be rounded to 4 decimal digits): $ P'=\Big($,,$ \Big)$
   

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  automatically generated: 2/ 6/2018