As I looked over the Wikipedia article on covariance and contravariance of vectors and $\mathbf{v}=v^i\mathbf{e}_i$ is said as a contravariant vector while $\mathbf{v}=v_i\mathbf{e}^i$ is said as covariant vector (or covector).
However, in the latter part, the article says:
Then the contravariant coordinates of any vector $\mathbf{v}$ can be obtained by the dot product of $\mathbf{v}$ with the contravariant basis vectors: $q^1=\mathbf{v}\cdot \mathbf{e}^1$, $q^2=\mathbf{v}\cdot \mathbf{e}^2$, and $q^3=\mathbf{v}\cdot \mathbf{e}^3$. Likewise, the covariant components of $\mathbf{v}$ can be obtained from the dot product of $\mathbf{v}$ with covariant basis vectors, viz. $q_1=\mathbf{v}\cdot \mathbf{e}_1$, $q_2=\mathbf{v}\cdot \mathbf{e}_2$, and $q_3=\mathbf{v}\cdot \mathbf{e}_3$.
I am getting confused. It seems that the location of the indices (up or down) of contravariant or covariant vectors is different in these two different parts.
Can anyone show me what the heck is this?
Thanks.