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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
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Verified Answer
The correct answer is:
$m_1\left(c_2-c_3\right)+m_2\left(c_3-c_1\right)+m_3\left(c_1-c_2\right)=0$
$\begin{aligned}
& \left|\begin{array}{lll}
m_1 & -1 & c_1 \\
m_2 & -1 & c_2 \\
m_3 & -1 & c_3
\end{array}\right|=0 \\
& \Rightarrow m_1\left(c_2-c_3\right)+m_2\left(c_3-c_1\right)+m_3\left(c_1-c_2\right)=0
\end{aligned}$
Note : Students should remember this question as a formula.
& \left|\begin{array}{lll}
m_1 & -1 & c_1 \\
m_2 & -1 & c_2 \\
m_3 & -1 & c_3
\end{array}\right|=0 \\
& \Rightarrow m_1\left(c_2-c_3\right)+m_2\left(c_3-c_1\right)+m_3\left(c_1-c_2\right)=0
\end{aligned}$
Note : Students should remember this question as a formula.
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