The value of $a$ for which the lines
$2 x + y - 1 = 0 a x + 3 y - 3 = 0 3 x + 2 y - 2 = 0$
are concurrent:

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Solution

Lines are concurrent if $∣ ∣ ∣ ∣ \begin{matrix} 2 & 1 & - 1 a & 3 & - 3 3 & 2 & - 2 \end{matrix} ∣ ∣ ∣ ∣ = 0$

Since $C_{2}$ and $C_{3}$ are propotional, lines are concurrent for infinite values of $a$

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