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Every Point on the Bisector of an Angle Is Equidistant from the Sides of the Angle.

The lines 2x ...

Question

The lines $2 x + y - 1 = 0$ , $a x + 3 y - 3 = 0$ and $3 x + 2 y - 2 = 0$ are concurrent for

All $a$

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$a = 4$ only

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$- 1 \leq a \leq 3$

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$a > 0$ only

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Solution

The correct option is A
All $a$

Find the value of $a$
Given, the equation of lines
$2 x + y - 1 = 0$
$a x + 3 y - 3 = 0$
$3 x + 2 y - 2 = 0$
Condition of concurrency $= |\begin{matrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{matrix}| = 0$
$\Rightarrow |\begin{matrix} 2 & 1 & - 1 \\ a & 3 & - 3 \\ 3 & 2 & - 2 \end{matrix}| \Rightarrow 2 (- 6 + 6) - 1 (- 2 a + 9) - 1 (2 a - 9) \Rightarrow 0 + 2 a - 9 - 2 a + 9 \Rightarrow 0$
Thus, the lines will be concurrent for all values of $a$
Hence, the correct option is $A$ .

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The equation of the line with slope $- \frac{3}{2}$ and which is concurrent with the lines $4 x + 3 y - 7 = 0$ and $8 x + 5 y - 1 = 0$ is

77 / 90

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

a

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

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