In $\mathbb { R } ^ { 3 }$, consider the planes $P _ { 1 } : y = 0$ and $P _ { 2 } : x + z = 1$. Let $P _ { 3 }$ be a plane, different from $P _ { 1 }$ and $P _ { 2 }$, which passes through the intersection of $P _ { 1 }$ and $P _ { 2 }$. If the distance of the point $( 0,1,0 )$ from $P _ { 3 }$ is 1 and the distance of a point $( \alpha , \beta , \gamma )$ from $P _ { 3 }$ is 2, then which of the following relations is (are) true? (A) $2 \alpha + \beta + 2 \gamma + 2 = 0$ (B) $2 \alpha - \beta + 2 \gamma + 4 = 0$ (C) $2 \alpha + \beta - 2 \gamma - 10 = 0$ (D) $2 \alpha - \beta + 2 \gamma - 8 = 0$
In $\mathbb { R } ^ { 3 }$, consider the planes $P _ { 1 } : y = 0$ and $P _ { 2 } : x + z = 1$. Let $P _ { 3 }$ be a plane, different from $P _ { 1 }$ and $P _ { 2 }$, which passes through the intersection of $P _ { 1 }$ and $P _ { 2 }$. If the distance of the point $( 0,1,0 )$ from $P _ { 3 }$ is 1 and the distance of a point $( \alpha , \beta , \gamma )$ from $P _ { 3 }$ is 2, then which of the following relations is (are) true?\\
(A) $2 \alpha + \beta + 2 \gamma + 2 = 0$\\
(B) $2 \alpha - \beta + 2 \gamma + 4 = 0$\\
(C) $2 \alpha + \beta - 2 \gamma - 10 = 0$\\
(D) $2 \alpha - \beta + 2 \gamma - 8 = 0$