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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
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$\frac{3}{x}+\frac{2}{y}+\frac{1}{z}=1$
$\frac{3}{x}+\frac{2}{y}+\frac{1}{z}=1$
If $a, b, \mathrm{c}$ are the intercepts of the variable plane on the $x, y, z$ axes respectively, then the equation of the plane is $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$ And the point of intersection of the planes parallel to the $x y, y z$ and $z x$ planes is ( $a, b$, c).
As the point $(3,2,1)$ lies on the variable plane, so $\frac{3}{a}+\frac{2}{b}+\frac{1}{c}=1$
Therefore, the required locus is $\frac{3}{x}+\frac{2}{y}+\frac{1}{z}=1$
As the point $(3,2,1)$ lies on the variable plane, so $\frac{3}{a}+\frac{2}{b}+\frac{1}{c}=1$
Therefore, the required locus is $\frac{3}{x}+\frac{2}{y}+\frac{1}{z}=1$
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