Find the vector equation of the plane through the intersection of the planes and and passing through the point (2, 1, -1).

Equation of plane through the line of intersection of two planes in vector form is

(1)

Where the standard equation of planes are

Putting values in equation(1)

(2)

Now as the plane passes through (2,1,-1)

Putting in equation (2)

2.1 + 1.(3 + λ) + (-1)(-1 + 2λ)=0

2 + 3 + λ + 1-2λ=0

λ=6

Putting the value of λ in equation (2)

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