#### Question

Find the equations of the planes parallel to the plane x-2y + 2z-4 = 0, which are at a unit distance from the point (1,2, 3).

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#### Solution

The equation of the planes parallel to the plane x −2y + 2z − 4 = 0

are of the form x-2y+2z+k=0

The distance of a plane ax+by+cz+ λ from a point (x_{1},y_{1},z_{1}) is given by

`d=|(9ax_1+by_1+cz_1+lambda)/sqrt(a^2+b^2+c^2)|`

It is given the plane x-2y+2z+k=0 at an unit distance from the point (1, 2, 3).

`d=|(1-2(2)+2(3)+k)/(sqrt(1^2+(-2)^2)+(2)^2)|`

`1=|(k+3)/3|`

∴ |k+3|=|3|

∴ k=0 or k=-6

The equation of the planes parallel to the plane x-2y+2z-4=0

are of x-2y+2z=0 and x-2y+2z=6

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#### Reference Material

Solution for question: Find the equations of the planes parallel to the plane x-2y + 2z-4 = 0, which are at a unit distance from the point (1,2, 3). concept: null - Equation of a Plane Passing Through Three Non Collinear Points. For the courses HSC Science (Computer Science), HSC Science (General) , HSC Arts, HSC Science (Electronics)