Question

If the distance between the points (a, 0, 1) and (0, 1, 2) is $\sqrt{27}$, then the value of 'a' is
(a) 5
(b) ±5
(c) –5
(d) none of these

Answer 1

Let A be given by (a, 0, 1) and B be given by (0, 1, 2)
Given:- Distance AB = $\sqrt{27}$
i.e $\sqrt{{\left(a-0\right)}^2+{\left(0-1\right)}^2+{\left(1-2\right)}^2}$ = $\sqrt{27}$ (By distance formula)
Now, By squaring both sides,
we get
a² + 1 + 1 = 27
i.e a² = 25
i.e a = ±5

Hence, the correct answer is option B.