Final answer:
The Cartesian equation of the plane parallel to 4x - 12y - 3z - 7 = 0 and passing through point A(2, -1, -4) is 4(x - 2) - 12(y + 1) - 3(z + 4) = 0.
Step-by-step explanation:
The question you've asked pertains to finding the Cartesian equation of a plane that is parallel to a given plane and passes through a specific point in three-dimensional space.
Given the plane equation 4x - 12y - 3z - 7 = 0, we can determine that its normal vector is (4, -12, -3).
A plane parallel to this will have the same normal vector.
Therefore, the equation of the plane we seek can be written as 4(x - x0) - 12(y - y0) - 3(z - z0) = 0, where (x0, y0, z0) is the point (2, -1, -4) through which the plane passes.
Plugging in these coordinates yields the Cartesian equation of the desired plane: 4(x - 2) - 12(y + 1) - 3(z + 4) = 0.