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To specify a vector in cartesian coordinate systems,we assume its tail to be at the origin and give the cartesian coordinates of its head.What about other coordinate systems?
For example,in spherical coordinates,is the following correct?
[itex]
a \hat{x}+b \hat{y}+c \hat{z}=\sqrt{a^2+b^2+c^2} \hat{r}+\cos^{-1}{\frac{c}{\sqrt{a^2+b^2+c^2}}}\hat{\theta}+\tan^{-1}{\frac{b}{a}}\hat{\varphi}
[/itex]
I know,it may seem so easy but the point that's making me doubt it,is the space dependent of the basis vectors in spherical coordinates.I just don't know can I just specify the point that the spherical coordinates of the vector are indicating and connect the origin to that point to show the vector or not!Another reason for doubting the process I explained,is the break down of spherical coordinates at the origin.
Thanks
For example,in spherical coordinates,is the following correct?
[itex]
a \hat{x}+b \hat{y}+c \hat{z}=\sqrt{a^2+b^2+c^2} \hat{r}+\cos^{-1}{\frac{c}{\sqrt{a^2+b^2+c^2}}}\hat{\theta}+\tan^{-1}{\frac{b}{a}}\hat{\varphi}
[/itex]
I know,it may seem so easy but the point that's making me doubt it,is the space dependent of the basis vectors in spherical coordinates.I just don't know can I just specify the point that the spherical coordinates of the vector are indicating and connect the origin to that point to show the vector or not!Another reason for doubting the process I explained,is the break down of spherical coordinates at the origin.
Thanks