Problems on equation of plane passing through intersection of two planes

Find the vector equation of a plane passing through the intersection of the planes vecr.(hati+hatj+hatk) = 6 and vecr. (2hati+3hatj+4hatk) - 5 = 0 and through the point (2,2,1) .

Find the equation of a plane passing through the intersection of the planes vecr . (hati+3hatj-hatk) = 5 and vecr.(2hati-hatj+hatk) = 3 and passes through the point (2,1,-2) .

Find the equation of a plane passing through the intersection of the planes x-3y+2z-5 - 0 and 2x+y+3z-1 = 0 and passes through the point (1,-2,3) .

Find the equation of the plane passing through the intersection of the planes 2x-3y+z-4=0 and x-y+z+1=0 and perpendicular to the plane x+2y-3z+6=0

The equation of the plane passing through the intersection of the planes 2x+y+2z=9,4x-5y-4z=1 and the point (3,2,1) is

The equation of plane passing through the intersection of the planes barr.(hati+hatj+hatk)=2and barr.(2hati+3hatj+hatk)=4 and parallel to X - axis is

The vector equation of the plane passing through the intersection of the planes barr.(hati+hatj+hatk)=8 and barr. (2hati+3hatj+4hatk)=3 and the point (1 , 0 , 2 ) is

Equation of plane passing through intersection of two planes and given point