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Equation of Planes Parallel to Axes

The equation ...

Question

The equation of plane passes through $(1, 2, 3)$ and perpendicular to the line $\frac{x}{2} = \frac{y}{3} = \frac{z}{1}$ is

x + 2 y + 3 z = 14

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x - 2 y - 3 z + 12 = 0

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3 x + 2 y + z = 8

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2 x + 3 y + z = 11

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Solution

The correct option is D $2 x + 3 y + z = 11$
As, the line $\frac{x}{2} = \frac{y}{3} = \frac{z}{1}$ is perpendicular to the plane
So, $D . r^{'} s$ os normal $= (a, b, c) = (2, 3, 1)$
So, equation is : $a (x - x_{1}) + b (y - y_{1}) + c (z - z_{1}) = 0$
$\Rightarrow 2 (x - 1) + 3 (y - 2) + 1 (z - 3) = 0 \Rightarrow 2 x + 3 y + z = 11$

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