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A plane P is parallel to two lines whose direction ratios are $‐ 2, 1, ‐ 3$ and $‐ 1, 2, ‐ 2$ and it contains the point $(2, 2, ‐ 2)$ . Let P intersect the co‐ordinate axes at the points A, B, C making the intercepts $α, β, γ .$ If V is the volume of the tetrahedron OABC, when O is the origin and $p = α + β + γ$ , , then the ordered pair $(V, p)$ is equal to

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$(48, ‐ 13)$

$(24, ‐ 13)$

$(48, 11)$

$(24, ‐ 5)$

answer is B.

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Detailed Solution

$| \begin{array}{ccc} x - 2 & y - 2 & z + 2 \\ - 2 & 1 & - 3 \\ - 1 & 2 & - 2 \end{array} | = 0 \Rightarrow 4 x - 8 - y + 2 - 32 - 6 = 0$

$\Rightarrow 4 x - y - 32 = 12 \Rightarrow \frac{x}{3} + \frac{y}{- 12} + \frac{z}{- 4} = 1$

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