The plane passing through the point (-2, -2, 2) and containing the line joining the points (1, 1, 1) and (1, -1, 2) makes intercepts on the coordinate axes, the sum of whose lengths is

Equation of the  required plane is ax+2+by+2+cz−2=0d.r.'s  of the line passing through Ax1,y1,z1,Bx2,y2,z2 are x2-x1,y2-y1,z2-z1 ∴d.r.'s of the line are <0,2,-1>⇒2b-c=0 and 3a+b=0 Put b=λ∴c=2λ;a=-λ3∴-λ3(x+2)+λ(y+2)+2λ(z-2)=0⇒−x+3y+6z−8=0⇒x−8+y83+z43=1∴sum of the lengths of the intercepts=8+83+43=12