Given.

A plane P contains the line of intersection of the plane

and

Now let. P 1 : x + y + z - 6 = 0

And P 2 : 2x + 3y+ 4z+5 = 0

So, by family of planes concept we get,

P : (x + y + z-6)+ (2z + 3y + 4z + 5)= 0

Also given plane P passes through (0, 2, - 2)

So. (0 + 2 - 2 - 6) + (4 + 6 - 8 + 5)= 0

Hence, equation of plane will be.

P: 5x + 7y + 9z + 4 = 0

Now distance of point (12,12,18) from plane win be.

And square of distance will be.

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