If the distance between the points (α,0,1) and (0, 1,2) is27, then the value of α is

A
5
B
-5
C
$\pm 5$
D
None of these

Solution:

Given, distance between points ( $α$ ,0,1 ) and (0, 1, 2) is $\sqrt{27}$

$\begin{array}{l} ∴ \sqrt{(a - 0)^{2} + (0 - 1)^{2} + (1 - 2)^{2}} = \sqrt{27} \\ \Rightarrow \sqrt{a^{2} + 1^{2} + 1^{2}} = \sqrt{27} \\ \Rightarrow a^{2} + 2 = 27 \\ [∵ squaring both sides] \\ \Rightarrow a^{2} = 25 \Rightarrow a = \pm 5 \end{array}$

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