A) \[a+b+c=0\]
B) \[a+b+c=1\]
C) \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=1\]
D) \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc=1\]
Correct Answer: D
Solution :
The planes are concurrent, therefore \[\left| \,\begin{matrix} -1 & c & b \\ c & -1 & a \\ b & a & -1 \\ \end{matrix}\, \right|=0\,\,\,\Rightarrow \,\,\,{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc=1\].
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