$\text{ A unit tangent vector at }t=2\text{ on the curve }x=t^2+2y=4t-5\text{ and }z=2t^2-6t\text{ is }$

$\begin{array}{l}\overrightarrow{\mathrm{r}}=\left({\mathrm{t}}^2+2\right)\widehat{\mathrm{i}}+(4\mathrm{t}-5)\widehat{\mathrm{j}}+\left(2{\mathrm{t}}^2-6\mathrm{t}\right)\widehat{\mathrm{k}}\\ \Rightarrow \frac{\mathrm{dr}}{\mathrm{dt}}=2\mathrm{t}\widehat{\mathrm{i}}+4\widehat{\mathrm{j}}+(4\mathrm{t}-6)\widehat{\mathrm{k}}\\ \Rightarrow {\left(\frac{\mathrm{d}\overrightarrow{\mathrm{r}}}{\mathrm{dt}}\right)}_{\mathrm{t}=2}=4\widehat{\mathrm{i}}+4\widehat{\mathrm{j}}+2\widehat{\mathrm{k}}\end{array}$

$\Rightarrow \text{ Unit tangent vector at }t=2\text{ is }\frac{1}{3}(2\widehat{i}+2\widehat{j}+\widehat{k})$