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?
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?
Updated On: Apr 25, 2024
- $\alpha+\beta=2$
- $\delta-\gamma=3$
- $\delta+\beta=4$
- $\alpha+\beta+\gamma=\delta$
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The Correct Option is A, B, C
Solution and Explanation
(A) $\alpha+\beta=2$
(B) $\delta-\gamma=3$
(C) $\delta+\beta=4$
(B) $\delta-\gamma=3$
(C) $\delta+\beta=4$
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