Upgrade to access all content for this subject

Let $V$ be the subspace spanned by the vector $u=\begin{bmatrix} 1\\\ 1\\\ -1\end{bmatrix}.$

Which of the following represents the orthogonal complement, $V^{\perp}$, of $V$?

The line $x=y=-z$.

$\mathbb{R}^3$

The subspace of all vectors $\begin{bmatrix} x\\\ y\\\ z\end{bmatrix}$ such that:

$$2x-3y+z=0$$

$$x+y-z=0$$