If $$S = \left\{ (x, y, z) \in \mathbb{E}^3 : x + y + z = 0 \right\}$$, then a Basis of S is​

Correct option is C

​$$\textbf{Solution: } \\S = \{(x, y, z) \in \mathbb{R}^3 \mid x + y + z = 0\} \\[6pt]\text{Solve the constraint: } x + y + z = 0 \Rightarrow x = -y - z \\[6pt]\text{So any vector in } S \text{ can be written as: } \\[4pt](x, y, z) = (-y - z, y, z) = y(-1, 1, 0) + z(-1, 0, 1) \\[6pt]\text{Hence, } \{(-1, 1, 0), (-1, 0, 1)\} \text{ is a basis of } S \\[6pt]\text{Final Answer: } \boxed{\{(-1, 1, 0), (-1, 0, 1)\}}$$​​