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

Question

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

Philoid · Accepted Answer

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 (1,1,1)

Putting in equation (2)

1.(1 + 2λ) + 1.(-1 + λ) + 1.(3-λ)=-1 + 5λ

1 + 2λ-1 + λ + 3- λ + 1-5λ=0

-3λ + 4=0

Putting the value of λ in equation (2)