The value(s) of a for which the lines 2x + y - 1 = 0; ax + 3y - 3 = 0 and 3x + 2y - 2 = 0 are concurrent, is/are:

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Solution

The correct option is E 5
$If three lines a_{1} x + b_{1} y + c_{1} = 0 a_{2} x + b_{2} y + c_{2} = 0 a_{3} x + b_{3} y + c_{3} = 0 are concurrent then, ⎛ ⎜ ⎝ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣ = 0$
$So, if the lines are concurrent, then$
$⎛ ⎜ ⎝ \begin{matrix} 2 & 1 & - 1 a & 3 & - 3 3 & 2 & - 2 \end{matrix} ∣ ∣ ∣ ∣ = 0 Since C_{2} and C_{3} are proportional, So, the lines will be concurrent for infinite values of a .$

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Similar questions

a

2 x + y - 1 = 0

a x + 3 y - 3 = 0

3 x + 2 y - 2 = 0

a

2 x + y - 1 = 0 a x + 3 y - 3 = 0 3 x + 2 y - 2 = 0

77 / 90

2 x + y - 1 = 0, a x + 3 y - 3 = 0

3 x + 2 y - 2 = 0

3 x + 4 y + 1 = 0, a x + 2 y - 3 = 0

2 x - y - 3 = 0

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