The equation of the plane which passes through the line of intersection of planes r→⋅n1→=q1,r→⋅n2→=q2 and  parallel to the line of intersection of planes r→⋅n3→=q3 and r→⋅n4→=q4 is

r→⋅n1→+λr→⋅n2→=q1+λq2----iSo n1→+λn2→ is normal to plane (i). Now, any planeparallel to the line of intersection of the planes r.→n3→=q3 and r→⋅n4→=q4 is of the form r→⋅n3→×n4→=dHence, we must have n→1+λn2→⋅n3→×n4→=0or  n1→n→3n→4+λn→2n→3n→4=0or  λ=−n→1n→3n→4n2→n3→n4→On putting this value in Eq. (i), we have the equation of the required plane as r→⋅n1→−q1=n→1n→3n4→n2→n3→n4→r⋅n2→−q2or  n2→n3→n4→r→⋅n→1−q1=n→1n→3n4r→⋅n2→−q2