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

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.