List of top Mathematics Questions on Orthogonal Complement asked in GATE ST

Let \( S = \{(x, y, z) \in \mathbb{R}^3 \setminus \{(0,0,0)\} : z = -(x + y)\} \). Denote:

\[ S^\perp = \{(p, q, r) \in \mathbb{R}^3 : px + qy + rz = 0 \text{ for all } (x, y, z) \in S\}. \]

Then which one of the following options is correct?