A sphere with center $\mathrm { C } ( 0,1,1 )$ and radius $2 \sqrt { 2 }$ intersects the line $\frac { x } { 2 } = y = - z$ at two points A and B. Let $S$ be the area of triangle CAB. Find the value of $S ^ { 2 }$.
A sphere with center $\mathrm { C } ( 0,1,1 )$ and radius $2 \sqrt { 2 }$ intersects the line $\frac { x } { 2 } = y = - z$ at two points A and B.\\
Let $S$ be the area of triangle CAB. Find the value of $S ^ { 2 }$.