If the given lines y = m_1 x + c_1 ,y = m_2 x + c_2 and y = m_3 x… - Vidyadip

MCQ

If the given lines $y = {m_1}x + {c_1},y = {m_2}x + {c_2}$ and $y = {m_3}x + {c_3}$ be concurrent, then

✓
${m_1}({c_2} - {c_3}) + {m_2}({c_3} - {c_1}) + {m_3}({c_1} - {c_2}) = 0$
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

✓

Answer

Correct option: A.

${m_1}({c_2} - {c_3}) + {m_2}({c_3} - {c_1}) + {m_3}({c_1} - {c_2}) = 0$

a
(a)$\left| {\begin{array}{*{20}{c}}{{m_1}}&{ - 1}&{{c_1}}\\{{m_2}}&{ - 1}&{{c_2}}\\{{m_3}}&{ - 1}&{{c_3}}\end{array}} \right| = 0$
==> ${m_1}({c_2} - {c_3}) + {m_2}({c_3} - {c_1}) + {m_3}({c_1} - {c_2}) = 0$.

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