A) \[{{r}^{2}}{{\cos }^{2}}\phi \]
B) \[{{r}^{2}}\sin \theta +{{r}^{2}}{{\cos }^{2}}\phi \]
C) \[{{r}^{2}}\]
D) \[\frac{1}{{{r}^{2}}}\]
Correct Answer: C
Solution :
\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}\] \[={{r}^{2}}{{\sin }^{2}}\theta {{\cos }^{2}}\phi +{{r}^{2}}{{\sin }^{2}}\theta {{\sin }^{2}}\phi +{{r}^{2}}{{\cos }^{2}}\theta \] \[={{r}^{2}}{{\sin }^{2}}\theta ({{\cos }^{2}}\phi +{{\sin }^{2}}\phi )+{{r}^{2}}{{\cos }^{2}}\theta \] \[={{r}^{2}}{{\sin }^{2}}\theta +{{r}^{2}}{{\cos }^{2}}\theta \] \[={{r}^{2}}({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )={{r}^{2}}\]
You need to login to perform this action.
You will be redirected in
3 sec
