Equation of the plane parallel to the plane $x + 2 y + 3 z = 5, x + 2 y + 3 z - 7 = 0$ and equidistant from them is

x + 2 y + 3 z = 6

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x + 2 y + 3 z = 1

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x + 2 y + 3 z + 6 = 0

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none of these

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Solution

The correct option is A $x + 2 y + 3 z = 6$
$x + 2 y + 3 z - 5 = 0, x + 2 y + 3 z - 7 = 0$ are given parallel planes.
Let the plane equidistant from them be $x + 2 y + 3 z + λ = 0$
Now, $λ = \frac{c_{1} + c_{2}}{2} = \frac{- 5 - 7}{2} = - 6$
i.e the equation of plane equidistant from them is
$x + 2 y + 3 z - 6 = 0$

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Similar questions

(- 1, 2, 0)

L_{1} : \frac{x}{3} = \frac{y + 1}{0} = \frac{z - 2}{- 1}

L_{2} : \frac{x - 1}{1} = \frac{2 y + 1}{2} = \frac{z + 1}{- 1}

The equation of the plane passing through the origin and perpendicular to the line x=2 y=3 z is

x + 2 y + 3 z - 5 = 0 = 3 x + 2 y + z - 5

x - 1 = 2 - y = z - 3

x - 2 y + 3 z = - (

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x^{4} - (2 y - 3 z)^{2} =

(x^{2} - 2 y + 3 z) (x^{2} + 2 y - 3 z)

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