Question

Let $\alpha, \beta, \gamma, \delta$ be real numbers such that $\alpha^{2}+\beta^{2}+\gamma^{2} \neq 0$ and $\alpha+\gamma=1$. Suppose the point $(3,2,-1)$ is the mirror image of the point $(1,0,-1)$ with respect to the plane $\alpha x+\beta y+\gamma z=\delta$. Then which of the following statements is/are TRUE?

• A. $\alpha+\beta=2$
• B. $\delta-\gamma=3$
• C. $\delta+\beta=4$
• D. $\alpha+\beta+\gamma=\delta$

Answer 1

Answer: (A), (B), (C)

$\alpha+\beta=2$

Answer 2

(A) $\alpha+\beta=2$
(B) $\delta-\gamma=3$
(C) $\delta+\beta=4$