The Cartesian equation of the plane passing through the point $(3, - 2, - 1)$ and parallel to the vectors $¯ ¯ b = ¯ i - 2 ¯ j + 4 ¯ ¯ ¯ k$ and $¯ ¯ c = 3 ¯ i + 2 ¯ j - 5 ¯ ¯ ¯ k$ is

2 x - 17 y - 8 z + 63 = 0

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3 x + 17 y + 8 z - 36 = 0

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2 x + 17 y + 8 z + 36 = 0

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3 x - 16 y + 8 z - 63 = 0

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Solution

The correct option is C $2 x + 17 y + 8 z + 36 = 0$
$∣ ∣ ∣ ∣ \begin{matrix} x - x_{1} & y - y_{1} & z - z_{1} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} \end{matrix} ∣ ∣ ∣ ∣ = 0$
$∣ ∣ ∣ ∣ \begin{matrix} x - 3 & y + 2 & z + 1 1 & - 2 & 4 3 & 2 & - 5 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$2 x + 17 y + 8 z + 36 = 0$

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