What is the condition for the vectors $2\hat{i} + 6\hat{j} - 8\hat{k}$ and $3\hat{i} - a\hat{j} + b\hat{k}$ to be parallel?

$\overline{\mathrm{P}}=2\widehat{\mathrm{i}}+6\widehat{\mathrm{j}}-8\widehat{\mathrm{k}},\mathrm{Q}=3\widehat{\mathrm{i}}-\mathrm{a}\widehat{\mathrm{j}}+\mathrm{b}\widehat{\mathrm{k}}$
For the vectors to be parallel
$\frac{{\mathrm{P}}_{\mathrm{x}}}{{\mathrm{Q}}_{\mathrm{x}}}=\frac{{\mathrm{P}}_{\mathrm{y}}}{{\mathrm{Q}}_{\mathrm{y}}}=\frac{{\mathrm{P}}_{\mathrm{z}}}{{\mathrm{Q}}_{\mathrm{z}}}\Rightarrow \frac{2}{3}=\frac{6}{-\mathrm{a}}=\frac{-8}{\mathrm{b}}$
On equating $\Rightarrow \frac{2}{3}=\frac{6}{-\mathrm{a}}\Rightarrow -2\mathrm{a}=18\Rightarrow \mathrm{a}=-9$
$\Rightarrow \frac{2}{3}=\frac{-8}{\mathrm{b}}\Rightarrow 2\mathrm{b}=-24\Rightarrow \mathrm{b}=-12$