If the points $(1,1, \lambda)$ and $(-3,0,1)$ are equidistant from the plane $3 x+4 y-12 z+13=0$, then integer value of $\lambda$ is

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Aicharya · Accepted Answer

Given $\mathrm{A}(1,1, \lambda)$ and $\mathrm{B}(-3,0,1)$ are equidistant from $3 \mathrm{x}+4 \mathrm{y}-12 \mathrm{z}+13=0$ $\begin{aligned} & 	herefore\left|\frac{3(1)+4(1)-12 \lambda+13}{\sqrt{9+16+144}}ight| \ & 	herefore\left|\frac{20-12 \lambda}{13}ight|=\left|\frac{-8}{13}ight| \ 	herefore & 20-12 \lambda=\pm 8 \ 	herefore & 20-12 \lambda=8 	ext { or } 20-12 \lambda=-8 \Rightarrow \lambda=1 	ext { or } \lambda=\frac{7}{3} \end{aligned}$

If the points $(1,1, \lambda)$ and $(-3,0,1)$ are equidistant from the plane $3 x+4 y-12 z+13=0$, then…

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