A) all values of\[x\]
B) only\[x=1\]
C) only\[x=0\]
D) None of these
Correct Answer: A
Solution :
\[\mathbf{a},\,\,\mathbf{b},\,\,\mathbf{c}\]are coplanar, if\[[\mathbf{a}\,\,\mathbf{b}\,\,\mathbf{c}]=0\] We have,\[[\mathbf{a}\,\,\mathbf{b}\,\,\mathbf{c}]=\left| \begin{matrix} x & x+1 & x+2 \\ x+3 & x+4 & x+5 \\ x+6 & x+7 & x+8 \\ \end{matrix} \right|\] \[=\left| \begin{matrix} x & x+1 & x+2 \\ 3 & 3 & 3 \\ 6 & 6 & 6 \\ \end{matrix} \right|\] \[[\because \]applying\[{{R}_{2}}\to {{R}_{2}}-{{R}_{1}},\,\,{{R}_{3}}\to {{R}_{3}}-{{R}_{1}}]\] \[=0,\,\,\forall x[\because \,\,{{R}_{2}}\]and \[{{R}_{3}}\] are proportional ]
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