The plane $2 x - y + z = 4$ intersects the line segment joining the points $\mathrm { A } ( \mathrm { a } , - 2,4 )$ and $\mathrm { B } ( 2 , \mathrm {~b} , - 3 )$ at the point C in the ratio 2 : 1 and the distance of the point C from the origin is $\sqrt { 5 }$. If $a b < 0$ and P is the point $( \mathrm { a } - \mathrm { b } , \mathrm { b } , 2 \mathrm {~b} - \mathrm { a } )$ then $\mathrm { CP } ^ { 2 }$ is equal to: (1) $\frac { 17 } { 3 }$ (2) $\frac { 16 } { 3 }$ (3) $\frac { 73 } { 3 }$ (4) $\frac { 97 } { 3 }$
The plane $2 x - y + z = 4$ intersects the line segment joining the points $\mathrm { A } ( \mathrm { a } , - 2,4 )$ and $\mathrm { B } ( 2 , \mathrm {~b} , - 3 )$ at the point C in the ratio 2 : 1 and the distance of the point C from the origin is $\sqrt { 5 }$. If $a b < 0$ and P is the point $( \mathrm { a } - \mathrm { b } , \mathrm { b } , 2 \mathrm {~b} - \mathrm { a } )$ then $\mathrm { CP } ^ { 2 }$ is equal to:
(1) $\frac { 17 } { 3 }$
(2) $\frac { 16 } { 3 }$
(3) $\frac { 73 } { 3 }$
(4) $\frac { 97 } { 3 }$