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(C) The equation of a plane parallel to $x - 2y + 2z = 5$ is of the form $x - 2y + 2z + k = 0$ ... $(i)$.The distance $d$ of a point $(x_1, y_1, z_1)$

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$x - 2y + 2z = 6$

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(C) The equation of a plane parallel to $x - 2y + 2z = 5$ is of the form $x - 2y + 2z + k = 0$ ... $(i)$.The distance $d$ of a point $(x_1, y_1, z_1)$ from the plane $Ax + By + Cz + D = 0$ is given by $d = \frac{|Ax_1 + By_1 + Cz_1 + D|}{\sqrt{A^2 + B^2 + C^2}}$.Given the point $(1, 2, 3)$ and distance $d = 1$,we have:$\frac{|1 - 2(2) + 2(3) + k|}{\sqrt{1^2 + (-2)^2 + 2^2}} = 1$$\frac{|1 - 4 + 6 + k|}{\sqrt{1 + 4 + 4}} = 1$$\frac{|k + 3|}{\sqrt{9}} = 1$$|k + 3| = 3$This implies $k + 3 = 3$ or $k + 3 = -3$.Case $1$: $k = 0$. Substituting into $(i)$,we get $x - 2y + 2z = 0$.Case $2$: $k = -6$. Substituting into $(i)$,we get $x - 2y + 2z - 6 = 0$,which is $x - 2y + 2z = 6$.Comparing with the given options,$x - 2y + 2z = 6$ is the correct equation.

The equation of the plane which is parallel to the plane $x - 2y + 2z = 5$ and whose distance from the point $(1, 2, 3)$ is $1$ is:

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