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Find the equation of the plane parallel ...

Find the equation of the plane parallel to the plane x - 2y + 2z - 3 = 0, which is at a unit distance from (1,2,3)

Text Solution

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Let the other plane parallel to given plane is,
`x-2y+2z+d =0`
As this plane is unit distance from (1,2,3)
`1 = +-(1**1 - 2**2 +2**3 +d)/sqrt(1^2+2^2+2^2)`
`1=+-(3+d)/3`
Solving above, we get `d=-6` and `d =0 `
So, equation of planes are:
`x-2y+2z=0` and `x-2y+2z-6 =0`
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