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प्रश्न
Prove that the following sets of three lines are concurrent:
3x − 5y − 11 = 0, 5x + 3y − 7 = 0 and x + 2y = 0
उत्तर
Given:
3x − 5y − 11 = 0 ... (1)
5x + 3y − 7 = 0 ... (2)
x + 2y = 0 ... (3)
Now, consider the following determinant:
\[\begin{vmatrix}3 & - 5 & - 11 \\ 5 & 3 & - 7 \\ 1 & 2 & 0\end{vmatrix} = 3 \times 14 + 5 \times 7 - 11 \times 7 = 0\]
Hence, the given lines are concurrent.
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