If the points A(2−x,2,2),B(2,2−y,2),C(2,2,2−z) and D(1,1,1) are coplanar, then  locus of P(x,y,z) is

Here AB→=OB→−OA=→xi^−yj^AC→=OC→−OA→=xi^−zk^AD→=OD→−OA→=(x−1)i^−j^−k^ As these vectors are coplanar, x−y0x0−zx−1−1−1=0⇒x(−z)+y(−x+xz−z)=0⇒xy+yz+zx=xyz⇒1x+1y+1z=1