\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows}

\begin{document}

\begin{tikzpicture}[
	>=stealth,
	auto,
	style={
		scale = 1
	}
	]

	\draw[->, thick, green] (-.87, -.5) -- (0, 0);
	\draw[->, thick, red] (-.87, .5) -- (0, 0);
	\draw[->, thick, blue] (.87, -1.5) -- (.87, -.5); 

	\draw[] (-.87, .5) circle[radius = 0]  node[left, scale = .95]{$x$};
	\draw[] (-.87, -.5) circle[radius = 0]  node[left, scale = .95]{$y$};
	\draw[] (.87, -1.5) circle[radius = 0]  node[below, scale = .95]{$z$};

	\draw[gray, dashed] (0, 0) -- (.87, -.5); 
	\draw[gray, dashed] (0, 0) -- (.87, .5); 
	\draw[gray, dashed] (.87, -.5) -- (.87, .5);

	\draw[->, thick, red] (.87, .5) -- (1.87, .5); 
	\draw[->, thick, blue] (.87, -.5) -- (1.87, -.5); 
	\draw[->, thick, green] (.87, .5) -- (.87, 1.5); 


	\draw[] (3.87, .5) circle[radius = 0]  node[left, scale = .95]{$x$};
	\draw[] (3.87, -.5) circle[radius = 0]  node[left, scale = .95]{$y$};
	\draw[] (4.87, -1.5) circle[radius = 0]  node[below, scale = .95]{$z$};

	\draw[->, thick, blue] (4.87, -1.5) -- (4.87, -.5); 
	\draw[->, thick, red] (3.87, .5) -- (4.87, .5); 
	\draw[->, thick, green] (3.87, -.5) -- (4.87, -.5); 
	\draw[->, thick, green] (4.87, .5) -- (4.87, 1.5); 
	\draw[->, thick, blue] (5.74, 0) -- (6.61, -.5); 
	\draw[->, thick, red] (5.74, 0) -- (6.61, .5); 

	\draw[gray, dashed] (4.87, -.5) -- (4.87, .5);
	\draw[gray, dashed] (4.87, -.5) -- (5.74, 0); 
	\draw[gray, dashed] (4.87, .5) -- (5.74, 0);


	\filldraw[fill=white, draw=black] (2.75, 0) circle [radius=0] node[scale = 2]{$=$};

	\filldraw[fill=white, draw=black] (-.44, -.275) circle [radius=0] node[below, scale = .7]{$i_1$};
	\filldraw[fill=white, draw=black] (.44, .275) circle [radius=0] node[above, scale = .7]{$i_2$};
	\filldraw[fill=white, draw=black] (1.45, .5) circle [radius=0] node[above, scale = .7]{$i_3$};
	\filldraw[fill=white, draw=black] (-.44, .275) circle [radius=0] node[above, scale = .7]{$j_1$};
	\filldraw[fill=white, draw=black] (.44, -.275) circle [radius=0] node[below, scale = .7]{$j_2$};
	\filldraw[fill=white, draw=black] (1.45, -.5) circle [radius=0] node[above, scale = .7]{$j_3$};
	\filldraw[fill=white, draw=black] (.87, -1) circle [radius=0] node[right, scale = .7]{$k_1$};
	\filldraw[fill=white, draw=black] (.87, 0) circle [radius=0] node[right, scale = .7]{$k_2$};
	\filldraw[fill=white, draw=black] (.87, 1) circle [radius=0] node[right, scale = .7]{$k_3$};

	\filldraw[fill=white, draw=black] (4.32, -.5) circle [radius=0] node[above, scale =.8]{$i_1$};
	\filldraw[fill=white, draw=black] (5.35, -.225) circle [radius=0] node[below, scale = .7]{$i_2$};
	\filldraw[fill=white, draw=black] (6.05, .225) circle [radius=0] node[above, scale = .7]{$i_3$};
	\filldraw[fill=white, draw=black] (4.32, .5) circle [radius=0] node[above, scale = .7]{$j_1$};
	\filldraw[fill=white, draw=black] (5.35, .225) circle [radius=0] node[above, scale = .7]{$j_2$};
	\filldraw[fill=white, draw=black] (6.05, -.225) circle [radius=0] node[below, scale = .7]{$j_3$};
	\filldraw[fill=white, draw=black] (4.87, -1) circle [radius=0] node[left, scale = .7]{$k_1$};
	\filldraw[fill=white, draw=black] (4.87, 0) circle [radius=0] node[left, scale = .7]{$k_2$};
	\filldraw[fill=white, draw=black] (4.87, 1) circle [radius=0] node[left, scale = .7]{$k_3$};


\end{tikzpicture}

\end{document}