A) \[x-y-z=1\]
B) \[x-2y-z=1\]
C) \[x-y-2z=1\]
D) \[2x-y-z=1\]
Correct Answer: D
Solution :
We have two spheres \[{{S}_{1}}={{x}^{2}}+{{y}^{2}}+{{z}^{2}}+7x-2y-z=13\] and \[{{S}_{2}}={{x}^{2}}+{{y}^{2}}+{{z}^{2}}=3x+3y+4z=8\] Intersection of \[{{S}_{1}}\] and \[{{S}_{2}}\] is given by \[{{S}_{1}}-{{S}_{2}}=0\] \[\Rightarrow \] \[7x+3x-2y-3y-z-4z=13-8\] \[\Rightarrow \] \[10x-5y-5z=5\] \[\Rightarrow \] \[2x-y-z=1\] (dividing by 5)
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