Let $S$ be the reflection of a point $Q$ with respect to the plane given by $$\vec { r } = - ( t + p ) \hat { \imath } + t \hat { \jmath } + ( 1 + p ) \hat { k }$$ where $t , p$ are real parameters and $\hat { \imath } , \hat { \jmath } , \hat { k }$ are the unit vectors along the three positive coordinate axes. If the position vectors of $Q$ and $S$ are $10 \hat { \imath } + 15 \hat { \jmath } + 20 \hat { k }$ and $\alpha \hat { \imath } + \beta \hat { \jmath } + \gamma \hat { k }$ respectively, then which of the following is/are TRUE ? (A) $3 ( \alpha + \beta ) = - 101$ (B) $3 ( \beta + \gamma ) = - 71$ (C) $3 ( \gamma + \alpha ) = - 86$ (D) $3 ( \alpha + \beta + \gamma ) = - 121$
Let $S$ be the reflection of a point $Q$ with respect to the plane given by
$$\vec { r } = - ( t + p ) \hat { \imath } + t \hat { \jmath } + ( 1 + p ) \hat { k }$$
where $t , p$ are real parameters and $\hat { \imath } , \hat { \jmath } , \hat { k }$ are the unit vectors along the three positive coordinate axes. If the position vectors of $Q$ and $S$ are $10 \hat { \imath } + 15 \hat { \jmath } + 20 \hat { k }$ and $\alpha \hat { \imath } + \beta \hat { \jmath } + \gamma \hat { k }$ respectively, then which of the following is/are TRUE ?\\
(A) $3 ( \alpha + \beta ) = - 101$\\
(B) $3 ( \beta + \gamma ) = - 71$\\
(C) $3 ( \gamma + \alpha ) = - 86$\\
(D) $3 ( \alpha + \beta + \gamma ) = - 121$