A) \[{{m}_{1}}({{c}_{2}}-{{c}_{3}})+{{m}_{2}}({{c}_{3}}-{{c}_{1}})+{{m}_{3}}({{c}_{1}}-{{c}_{2}})=0\]
B) \[{{m}_{1}}({{c}_{2}}-{{c}_{1}})+{{m}_{2}}({{c}_{3}}-{{c}_{2}})+{{m}_{3}}({{c}_{1}}-{{c}_{3}})=0\]
C) \[{{c}_{1}}({{m}_{2}}-{{m}_{3}})+{{c}_{2}}({{m}_{3}}-{{m}_{1}})+{{c}_{3}}({{m}_{1}}-{{m}_{2}})=0\]
D) None of these
Correct Answer: A
Solution :
\[\left| \begin{matrix} {{m}_{1}} & -1 & {{c}_{1}} \\ {{m}_{2}} & -1 & {{c}_{2}} \\ {{m}_{3}} & -1 & {{c}_{3}} \\ \end{matrix} \right|=0\] Þ \[{{m}_{1}}({{c}_{2}}-{{c}_{3}})+{{m}_{2}}({{c}_{3}}-{{c}_{1}})+{{m}_{3}}({{c}_{1}}-{{c}_{2}})=0\]. Note: Students should remember this question as a formula.
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