A) \[0\]
B) \[1\]
C) \[-1\]
D) None of these
Correct Answer: C
Solution :
[c] \[a=x/(y-z)\Rightarrow x-ay+az=0...(1)\] \[b=y/(z-x)\Rightarrow bx+y-bz=0...(2)\] \[c=z/(x-y)\Rightarrow -cx+cy+z=0...(3)\] As x, y, z are not all zero, the above system has a non-trivial solution so \[\Delta =\left| \begin{matrix} 1 & -a & a \\ b & -1 & -b \\ -c & c & 1 \\ \end{matrix} \right|\] \[\therefore 1+ab+bc+ca=0\]
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