The equation of plane passing through the point $(1, 1, 1)$ and perpendicular to the planes $2 x + y - 2 z = 5$ and $3 x - 6 y - 2 z = 7$ is

14 x + 2 y - 15 z = 1

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14 x - 2 y + 15 z = 27

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14 x + 2 y + 15 z = 31

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- 14 x + 2 y + 15 z = 3

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Solution

The correct option is B $14 x + 2 y + 15 z = 31$
$∣ ∣ ∣ ∣ \begin{matrix} x - 1 & y - 1 & z - 1 2 & 1 & - 2 3 & - 6 & - 2 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$\Rightarrow (x - 1) (- 14) - (y - 1) (2) + (z - 1) (- 15) = 0$
$\Rightarrow 14 x - 14 + 2 y - 2 + 15 z - 15 = 0$
$14 x + 2 y + 15 z = 31$

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Similar questions

The equation of the plane passing through the point (1,1,1) and perpendicular to the planes 2x+y-2z=5 and 3x-6y-2z=7 is

(1, 1, 1)

2 x + y - 2 z = 5

3 x - 6 y - 2 z = 7

The equation of the plane passing through the point (1,1,1) and perpendicular to the planes 2x+y-2z=5 and 3x-6y-2z=7 is

(1, - 1)

x + 2 y + 3 = 0

3 x + 4 y + 5 = 0

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