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A plane $\pi$ makes intercepts 3 and 4 respectively on $Z$-axis and $X$-axis. If $\pi$ is parallel to $Y$-axis, then its equation is :
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Verified Answer
The correct answer is:
$3 x+4 z=12$
Given that $a=4, c=3$
Equation of the plane ' $\pi$ ' is
$\frac{x}{a}+\frac{y}{b}+\frac{z}{b}=1 \Rightarrow \frac{x}{4}+\frac{y}{b}+\frac{z}{3}=1$
Since, $\pi$ is parallel to $Y$-axis.
$\therefore \quad \frac{0 \cdot \frac{1}{a}+1 \cdot \frac{1}{b}+0 \cdot \frac{1}{c}}{\sqrt{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}}}=0 \Rightarrow \frac{1}{b}=0$
Thus, the equation of plane $\pi$ is
$\frac{x}{4}+\frac{z}{3}=1 \Rightarrow 3 x+4 z-12=0$
Equation of the plane ' $\pi$ ' is
$\frac{x}{a}+\frac{y}{b}+\frac{z}{b}=1 \Rightarrow \frac{x}{4}+\frac{y}{b}+\frac{z}{3}=1$
Since, $\pi$ is parallel to $Y$-axis.
$\therefore \quad \frac{0 \cdot \frac{1}{a}+1 \cdot \frac{1}{b}+0 \cdot \frac{1}{c}}{\sqrt{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}}}=0 \Rightarrow \frac{1}{b}=0$
Thus, the equation of plane $\pi$ is
$\frac{x}{4}+\frac{z}{3}=1 \Rightarrow 3 x+4 z-12=0$
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