I recently started studying inner products, norms and orthonormal vectors and bases to find the projection of a vector.
I have a problem in this statement: Given, $V=\mathbb{R}^2$ and is an inner product space, $W\subset V$ and $W= \text{span}\lbrace (2,1) \rbrace$, then $\langle(2,1) \rangle$ is orthogonal. Here, $\langle\cdot,\cdot \rangle$ denote standard inner product which is the dot product.
I understand that for a set $V=\{v_1,v_2,...,v_k\}$ to be orthgonal, $\langle v_i,v_j \rangle=0$ for $i\neq j$. As per me, for $\langle(2,1) \rangle$ to be orthogonal, either we are performing $\langle (2,1),(0,0) \rangle$ or it's true by definition.
It would be helpful if someone could explain this.
Regards