The equation of the 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

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TestHub · Accepted Answer

The normal vector of required plane is parallel to vector

$= |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 1 & - 2 \\ 3 & - 6 & -2 \end{matrix}| = - 14 \hat{i} - 2 \hat{j} - 15 \hat{k}$

$∴$ The equation of required plane passing through (1, 1, 1) will be $- 14 (x - 1) - 2 (y - 1) - 15 (z - 1) = 0$

$\Rightarrow 14 x + 2 y + 15 z = 31$

$∴$ option $14 x + 2 y + 15 z = 31$ is correct.

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