Consider two intersecting lines $L_{1} = 0$ and $L_{2} = 0$ . Which of the following does not represent pair of straight lines ?

L_{1} L_{2} = 0

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L_{1}^{2} + L_{2}^{2} = 0

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L_{1}^{2} - L_{2}^{2} = 0

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(L_{1} + L_{2})^{2} = (L_{1} - L_{2})^{2}

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Solution

The correct option is C $L_{1}^{2} - L_{2}^{2} = 0$
$\begin{matrix} L_{1}^{2} - L_{2}^{2} = 0 L_{1} = L_{2} \end{matrix}$
does not represent the pair of line

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Similar questions

lf $θ$ is the angle between two lines whose d.cs are $l_{1}, m_{1}, n_{1}$ and $l_{2}, m_{2}, n_{2}$ , then

$\frac{Σ (l_{1} + l_{2})^{2}}{4 {cos}^{2} (\frac{θ}{2})} + \frac{Σ (l_{I} - l_{2})^{2}}{4 {sin}^{2} (\frac{θ}{2})} =$

⎡ ⎢ ⎣ \begin{matrix} l_{1} & m_{1} & n_{1} l_{2} & m_{2} & n_{2} l_{3} & m_{3} & n_{3} \end{matrix} ⎤ ⎥ ⎦

l_{1}^{2} + m_{1}^{2} + n_{1}^{2} = \sum l_{1}^{2} = 1 = \sum l_{2}^{2} = \sum l_{3}^{2}

l_{1} l_{2} + m_{1} m_{2} + n_{1} n_{2} = \sum l_{1} l_{2} = 0 = \sum l_{2} l_{3} = \sum l_{3} l_{1}

l_{1} a n d l_{2}

l_{1}, m_{1}, n_{1}; l_{2}, m_{2}, n_{2}; l_{3}, m_{3}, n_{3}

l_{1}^{2} + m_{1}^{2} + n_{1}^{2} = l_{2}^{2} + m_{2}^{2} + n_{2}^{2} = l_{3}^{2} + m_{3}^{2} + n_{3}^{2} = 1

l_{2} l_{3} + m_{2} m_{3} + n_{2} n_{3} = l_{3} l_{1} + m_{3} m_{1} + n_{3} n_{1} = l_{1} l_{2} + m_{1} m_{2} + n_{1} n_{2} = 0

∣ ∣ ∣ ∣ \begin{matrix} l_{1} & m_{1} & n_{1} l_{2} & m_{2} & n_{2} l_{3} & m_{3} & n_{3} \end{matrix} ∣ ∣ ∣ ∣ = \pm k

k

Find the equation of the circle circumscribing the triangle formed by the lines $L_{1} = 0, L_{2} = 0$ and $L_{3} = 0$

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