The orthogonal complement of $W\subseteq V$ is $W^\perp=\{x\in V:\langle w,x\rangle=0\text{ for every }w\in W\}$. It is a subspace. In a finite-dimensional inner-product space, $\dim W^\perp=\dim V-\dim W$ and $V=W\oplus W^\perp$.
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