If the distance between the points ($\mathrm{\alpha }$,0,1) and (0, 1,2) is$\sqrt{27}$, then the value of $\mathrm{\alpha }$ is

Solution:

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

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