The equation of a plane parallel to the plane | vedclass

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Question

(A) Let the equation of the plane parallel to $x - 2y + 2z - 5 = 0$ be $x - 2y + 2z + k = 0 \dots (i)$The perpendicular distance from the origin $(0,

Vedclass · Accepted Answer

$x - 2y + 2z - 3 = 0$

Vedclass · Answer

(A) Let the equation of the plane parallel to $x - 2y + 2z - 5 = 0$ be $x - 2y + 2z + k = 0 \dots (i)$The perpendicular distance from the origin $(0, 0, 0)$ to the plane $(i)$ is given by the formula $d = \frac{|k|}{\sqrt{a^2 + b^2 + c^2}}$.Given that the distance is $1$,we have:$\frac{|k|}{\sqrt{1^2 + (-2)^2 + 2^2}} = 1$$\frac{|k|}{\sqrt{1 + 4 + 4}} = 1$$\frac{|k|}{\sqrt{9}} = 1$$\frac{|k|}{3} = 1$$|k| = 3$Therefore,$k = 3$ or $k = -3$.Substituting these values into equation $(i)$,we get the possible equations of the plane as $x - 2y + 2z + 3 = 0$ or $x - 2y + 2z - 3 = 0$.Comparing this with the given options,the correct equation is $x - 2y + 2z - 3 = 0$.

The equation of a plane parallel to the plane $x - 2y + 2z - 5 = 0$ and at a unit distance from the origin is:

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