If the distance between the points (a, 0, 1)


If the distance between the points (a, 0, 1) and (0, 1, 2) is √27, then the value of a is (A) 5 (B) ± 5 (C) – 5 (D) none of these


(B) ± 5


Let $\mathrm{P}$ be the point whose coordinate is $(\mathrm{a}, 0,1)$ and $\mathrm{Q}$ represents the point $(0$, $1,2)$.

Given, $P Q=V 27$

From distance formula we have

$P Q=\sqrt{(a-0)^{2}+(0-1)^{2}+(1-2)^{2}}=\sqrt{a^{2}+2}$

$\Rightarrow \sqrt{27}=\sqrt{a^{2}+2}$

Squaring on both sides


$\Rightarrow a^{2}=25$

$\Rightarrow a=\pm \sqrt{25}=\pm 5$

$\therefore \mathrm{a}=5$ or $\mathrm{a}=-5$

Option (A) and(C) both have one correct answer but only option(B)contains both the answers Hence, option(B) is the most suitable choice.

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