An equation of a plane parallel to the plane | vedclass

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Question

(B) The equation of a plane parallel to $x-2y+2z-5=0$ is of the form $x-2y+2z+k=0$. The distance of this plane from the origin $(0,0,0)$ is given by t

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) The equation of a plane parallel to $x-2y+2z-5=0$ is of the form $x-2y+2z+k=0$. The distance of this plane from the origin $(0,0,0)$ is given by the formula $d = \frac{|k|}{\sqrt{1^2+(-2)^2+2^2}}$. Given that the distance $d = 1$,we have $1 = \frac{|k|}{\sqrt{1+4+4}}$,which simplifies to $1 = \frac{|k|}{\sqrt{9}}$. Thus,$1 = \frac{|k|}{3}$,which implies $|k| = 3$,so $k = \pm 3$. Therefore,the possible equations are $x-2y+2z+3=0$ or $x-2y+2z-3=0$. Comparing this with the given options,$x-2y+2z-3=0$ is the correct choice.

An equation of a plane parallel to the plane $x-2y+2z-5=0$ and which is at a distance of $1$ unit from the origin is:

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