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# A plane passes through the points $(2,0,0) (0,3,0)$ and $(0,0,4)$.The equation of plane is__________.

$\begin{array}{1 1} (A)\;\large\frac{x}{2}+\frac{y}{3}-\frac{z}{4}=1 \\(B)\;\large\frac{x}{8}+\frac{y}{7}+\frac{z}{4}=1 \\ (C)\;\large\frac{x}{2}+\frac{y}{3}+\frac{z}{4}=1 \\ (D)\;\large\frac{x}{2}-\frac{y}{3}-\frac{z}{4}=1 \end{array}$

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• The cartesian equation of a plane intercepting length $a,b$ and $c$ with $x,y$ and $z$ axes $\large\frac{x}{a}+\frac{y}{b}+\frac{z}{c}$$=1 The given points are A(2,0,0),B(0,3,0) and C(0,0,4) Here it is clear that the intercepting length a,b,c with the x,y,z axes is 2,3,4 Therefore The equation of the plane is \large\frac{x}{2}+\frac{y}{3}+\frac{z}{4}$$=1$