Equation of the plane passing through the origin and perpendicular to the planes x+2y+z=1,3x-4y+z = 5 is

x + 2y - 5z = 0

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x - 2y - 3z = 0

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x - 2y + 5z = 0

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3x + y - 5z = 0

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Solution

The correct option is D 3x + y - 5z = 0
$∣ ∣ ∣ ∣ \begin{matrix} x & y & z 1 & 2 & 1 3 & - 4 & 1 \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow 3 x + y - 5 z = 0$

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