A variable plane passes through a fixed point ( $3,2,1$ ) and meets $x , y$ and $z$ axes at $A , B$ and $C$ respectively. A plane is drawn parallel to $y z$ - plane through $A$, a second plane is drawn parallel $z x$ plane through $B$ and a third plane is drawn parallel to $x y$ - plane through $C$. Then the locus of the point of intersection of these three planes, is (1) $( x + y + z = 6 )$ (2) $\frac { x } { 3 } + \frac { y } { 2 } + \frac { z } { 1 } = 1$ (3) $\frac { 3 } { x } + \frac { 2 } { y } + \frac { 1 } { z } = 1$ (4) $\frac { 1 } { x } + \frac { 1 } { y } + \frac { 1 } { z } = \frac { 11 } { 6 }$
A variable plane passes through a fixed point ( $3,2,1$ ) and meets $x , y$ and $z$ axes at $A , B$ and $C$ respectively. A plane is drawn parallel to $y z$ - plane through $A$, a second plane is drawn parallel $z x$ plane through $B$ and a third plane is drawn parallel to $x y$ - plane through $C$. Then the locus of the point of intersection of these three planes, is\\
(1) $( x + y + z = 6 )$\\
(2) $\frac { x } { 3 } + \frac { y } { 2 } + \frac { z } { 1 } = 1$\\
(3) $\frac { 3 } { x } + \frac { 2 } { y } + \frac { 1 } { z } = 1$\\
(4) $\frac { 1 } { x } + \frac { 1 } { y } + \frac { 1 } { z } = \frac { 11 } { 6 }$