Add vertical space in tabular cells

Here is one way to do it: treat the second row in the first header entry as a second row.

\documentclass[11pt]{article} \begin{document} \begin{center} \begin{tabular}{c|c|c} \hline \rule{0pt}{3ex} Ratio of unit lengths & % first row Tan. \phi & Tan. \theta \\ $u_x : u_y : u_z$ & & \\ % second row [1ex] \hline \rule{0pt}{5ex} $\left\{ \begin{tabular}{c} 1{\hspace{1em}:\hspace{1em}}1{\hspace{1em}:\hspace{1em}}1 \\ \textrm{Isometric} \end{tabular}\right\}$ & $\phi = \theta$ & = $60^\circ$ \\ [3ex] \begin{tabular}{c@{\hspace{1em}:\hspace{1em}}c@{\hspace{1em}:\hspace{1em}}r} 2 & 1 & 2 \\ 3 & 1 & 3 \\ 4 & 1 & 4 \\ 5 & 4 & 6 \\ 6 & 5 & 10 \end{tabular} & \begin{tabular}{r@{\hspace{1em}:\hspace{1em}}c} 8 & 1 \\ 18 & 1 \\ 32 & 1 \\ 5 & 1 \\ 11 & 1 \end{tabular} & \begin{tabular}{r@{\hspace{1em}:\hspace{1em}}c} 8 & 7 \\ 18 & 17 \\ 32 & 31 \\ 3 & 1 \\ 5 & 8 \end{tabular} \\ \hline \end{tabular} \end{center} \end{document} 

Result:

To center the 2nd and 3rd header also vertically you might need a different table package. There is a way to do it with tabular using m{width}, but it works like p{width} i.e. aligns left, while you wanted center c.