Snagged a little on some vector math

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The discussion focuses on the calculation of electric fields (E-fields) using unit vectors in vector mathematics. Specifically, the radial unit vector is defined as \(\hat{r} = \vec{r}/r\), where in Cartesian coordinates, \(\hat{r} = (x/r, y/r, z/r)\) and \(r = \sqrt{x^2 + y^2 + z^2}\). The user seeks clarification on the algebra involved in using unit vectors with single components, such as \(r^x = x/r\). This highlights the importance of understanding vector normalization in physics.

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I'm learning how to calculate E-fields and, in some examples, when using the unit vector r^ with only one component (ie r^x or r^y), it is simply defined r^x=x/r. I am missing the algebra. Will anyone explain this to me? Thanks
 
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Bei definition the radial unit vector ist [itex]\hat{r}=\vec{r}/r[/itex]. In Cartesian coordinates, you have [itex]\hat{r}=(x/r,y/r,z/r)[/itex] with [itex]r=\sqrt{x^2+y^2+z^2}[/itex].
 

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