in n -imensional linear space,e_i are the standard Orthogonal basic, we use the axiom of clifford algebra : $x\cdot y = \frac{1}{2}(xy+yx) ,x\wedge y = \frac{1}{2}(xy-yx), xy=x\cdot y + x\wedge y$ to deduce(i,j,k are not the same, so $e_i\cdot e_j = 0$ and so on) : and we have $e_ie_j=-e_je_i$ so $e_ie_je_k=e_ke_ie_j$
$(e_i\wedge e_j)\cdot e_k = \\ (e_ie_j-e_i\cdot e_j)\cdot e_k = \\ (e_ie_j)\cdot e_k=\\ \frac{1}{2}(e_ie_je_k+e_ke_ie_j)=\\ e_ie_je_k = (e_i\wedge e_j)\cdot e_k + (e_i\wedge e_j)\wedge e_k \Rightarrow \\ e_i\wedge e_j\wedge e_k = 0$
but $e_i\wedge e_j\wedge e_k \neq 0$ ,so where is the problem??