Which of the following is true about the three lines
$L_{1} : x - 3 y + 7 = 0, L_{2} : 2 x + y - 3 = 0$ and $L_{3} : 7 x + \frac{7 y}{2} - \frac{21}{2} = 0$

Lines form a triangle

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Lines are concurrent

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Lines can not bound any region

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None of these

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Solution

The correct option is B Lines can not bound any region
Given equations of lines as
$L_{1} : x - 3 y + 7 = 0$
Slope of $L_{1} = \frac{1}{3}$
$L_{2} : 2 x + y - 3 = 0$
Slope of $L_{2} = - 2$
$L_{3} : 7 x + \frac{7 y}{2} - \frac{21}{2} = 0$
Slope of $L_{3} = - 2$
$\Rightarrow L_{2}$ and $L_{3}$ are parallel
Hence, lines cannot bound any region.

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