Given that the plane passes through point m (1, - 1,1) n (0,1, - 3) and is parallel to vector a (1,1,1), the plane equation is solved | Math enthusiast | Mathematical art

Given that the plane passes through point m (1, - 1,1) n (0,1, - 3) and is parallel to vector a (1,1,1), the plane equation is solved

Let ax + by + CZ + D = 0
A-B+C+D=0
B-3C+D=0
A+B+C= 0 => 2B-D=0 => D=2B
=>C=(B+D)/3 => C=B
A=-(B+C) => A=-2B
Take B = - 1
Then a = 2, B = - 1, C = - 1, d = - 2
The plane equation 2x-y-z-2 = 0 is obtained

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