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Mathematics · 2022 · 2 marks
CBSE 2022 · Region 3 · Set 2 · Q5
If the distance of the point (1,1,1) from the plane x- y + z +λ=0 is 5/(√ 3), find the value (s) of λ.
If the distance of the point ($\displaystyle 1,1,1$) from the plane $\displaystyle x-\mathrm{y}+\mathrm{z}+\lambda=0$ is $\displaystyle \frac{5}{\sqrt{3}}$, find the value (s) of $\displaystyle \lambda$.
Marking-scheme solution
Distance of point ($\displaystyle 1$, $\displaystyle 1$, $\displaystyle 1$) from \(\displaystyle x-y+z+\lambda=0\) is
\[\frac{|1+\lambda|}{\sqrt{3}}
\]
\[\frac{|1+\lambda|}{\sqrt{3}}=\frac{5}{\sqrt{3}} \Rightarrow 1+\lambda= \pm 5
\]
\[\lambda=-6 \text { or }+4
\]
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CBSE Class 12 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.