\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{tikz}
\usepackage{tikz-3dplot}

\begin{document}
\begin{preview}
	\tdplotsetmaincoords{70}{110}

	\begin{tikzpicture}[scale=3,tdplot_main_coords]
		\draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
		\draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
		\draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};
		\tdplotsetcoord{O}{0}{0}{0}
		\tdplotsetcoord{P}{.8}{50}{70}

		%draw a vector from origin to point (P)
		\draw[-stealth,color=red] (O) -- (P);

		%draw projection on xy plane, and a connecting line
		\draw[dashed, color=red] (O) -- (Pxy);
		\draw[dashed, color=red] (P) -- (Pxy);
		\tdplotsetthetaplanecoords{70}
		\draw[tdplot_rotated_coords,color=blue,thick,->] (0,0,0)
		-- (.2,0,0) node[anchor=east]{$x'$};
		\draw[tdplot_rotated_coords,color=blue,thick,->] (0,0,0)
		-- (0,.2,0) node[anchor=north]{$y'$};
		\draw[tdplot_rotated_coords,color=blue,thick,->] (0,0,0)
		-- (0,0,.2) node[anchor=west]{$z'$};
	\end{tikzpicture}
\end{preview}
\end{document}