Question:
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
Solution:
(B) ± 5
Explanation:
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
$a^{2}+2=27$
$\Rightarrow a^{2}=25$
$\Rightarrow a=\pm \sqrt{25}=\pm 5$
$\therefore \mathrm{a}=5$ 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.