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which of the following is not correct for the planes $L_{1} : 2 (x - 1) + 3 (y + 2) + (z - 7) = 0$ and $L_{1} : 2 (x + 1) - 3 (y + 2) + (z + 7) = 0$

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$L_{1}$ and $L_{2}$ are equidistant from the origin

$L_{1}$ and $L_{2}$ are not perpendicular

Equation of a plane through the intersection of $L_{1}$ and $L_{2}$ is $y = 0$

$L_{1}$ and $L_{2}$ are parallel

answer is B, C.

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Detailed Solution

$L_{1} : 2 x + 3 y + z - 3 = 0, L_{2} : 2 x - 3 y + z + 3 = 0$

Distance of $L_{1}$ from the origin $= |\frac{- 3}{\sqrt{2^{2} + 3^{2} + 1^{2}}}|$

Distance of $L_{2}$ from the origin $= |\frac{3}{\sqrt{2^{2} + (- 3)^{2} + 1^{2}}}|$

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