Let S = (x, y, z) in R^3 setminus (0,0,0) : z = -(x + y). Denote S^perp = (p, q, r) in R^3 : px + qy + rz = 0 for all (x, y, z) in S. Then which one of the following options is correct?

Q13Section ST (Statistics (Q11–Q65))13 of 65

Orthogonal complement of a punctured plane

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?

Pick an option to check your answer. In a mock test a wrong answer here costs 1/3 mark.

Keyboard: A–D answer · S solution · ←/→ previous/next