For what value of t, the points (2, –1, 3), (3, –5, t) and (–1, 11, 9) are collinear?

Given points A = (2, –1, 3), B =(3, –5, t) C = (–1, 11, 9)
A, B, C are collinear then
$\begin{array}{l}\frac{{\mathrm{x}}_2-{\mathrm{x}}_1}{{\mathrm{x}}_3-{\mathrm{x}}_1}=\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{y}}_3-{\mathrm{y}}_1}=\frac{{\mathrm{z}}_2-{\mathrm{z}}_1}{{\mathrm{z}}_3-{\mathrm{z}}_1}\\ \frac{3-2}{-1-2}=\frac{-5+1}{11+1}=\frac{\mathrm{t}-3}{9-3}\Rightarrow \frac{1}{-3}=\frac{-4}{12}=\frac{\mathrm{t}-3}{6}\\ \Rightarrow \frac{\mathrm{t}-3}{6}=-\frac{1}{3}\Rightarrow \mathrm{t}-3=-2\\ \Rightarrow \mathrm{t}=3-2\Rightarrow \mathrm{t}=1\end{array}$