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