Find the equation of the plane through the point and passing through the line of intersection of the planes and

we know that, the equation of a plane passing through the line of intersection of two planes


and


is given by


So the equation of the plane passing through the line of intersection of given two planes


and is given by


…… (1)


As given that, plane (1) is passing through the point 2 so



(2)(1) + (1)(3) + ( – 1)( – 1) + k[(2)(0) + (1)(1) + ( – 1)(2)] = 0


(2 + 3 + 1) + k(1 – 2) = 0


6 – k = 0


k = 6


put the value of k in equation (1)






So, the equation of the required plane is


4