Find the Cartesian equation of the plane through the points A(2,–1,–4) and parallel to the plane 4x–12y–3z

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Find the Cartesian equation of the plane through the points $A (2, - 1, - 4)$ and parallel to the plane $4 x - 12 y - 3 z - 7 = 0 .$

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Detailed Solution

The Cartesian equation of the plane through the point $A (2, - 1, - 4)$ and parallel to the plane

$4 x - 12 y - 3 z - 7 = 0$ is

$4 (x - 2) - 12 (y + 1) - 3 (z + 4) = 0$

$\Rightarrow 4 x - 8 - 12 y - 12 - 3 z - 12 = 0$

$\Rightarrow 4 x - 12 y - 3 z - 32 = 0$

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