A) \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}={{r}^{2}}\]
B) \[{{x}^{2}}+{{y}^{2}}-{{z}^{2}}={{r}^{2}}\]
C) \[{{x}^{2}}-{{y}^{2}}+{{z}^{2}}={{r}^{2}}\]
D) \[{{z}^{2}}+{{y}^{2}}-{{x}^{2}}={{r}^{2}}\]
Correct Answer: A
Solution :
\[x=r\]\[x=r\,\sin \theta \,\cos \phi \] ......(i) \[y=r\,\sin \theta \sin \phi \] ?..(ii) \[z=r\cos \theta \] ?..(iii) Squaring and adding (i) and (ii), we get \[{{x}^{2}}+{{y}^{2}}={{r}^{2}}{{\sin }^{2}}\theta \] Squaring (iii) and adding it with (iv), we get \[{{x}^{2}}+{{z}^{2}}+{{y}^{2}}={{r}^{2}}\]
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