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Let $S$ be the reflection of a point $Q$ with respect to the plane given by $\vec{r}=-(t+p) \hat{ i }+t \hat{ j }+(1+p) \hat{ k }$ where $t, p$ are real parameters and $\hat{ i }, \hat{ j }, \hat{ k }$ are the unit vectors along the three positive coordinate axes If the position vectors of $Q$ and $S$ are $10 \hat{ i }+15 \hat{ j }+20 \hat{ k }$ and $\alpha \hat{ i }+\beta \hat{ j }+\gamma \hat{ k }$ respectively, then which of the following is/are TRUE ?
Let $S$ be the reflection of a point $Q$ with respect to the plane given by $\vec{r}=-(t+p) \hat{ i }+t \hat{ j }+(1+p) \hat{ k }$ where $t, p$ are real parameters and $\hat{ i }, \hat{ j }, \hat{ k }$ are the unit vectors along the three positive coordinate axes If the position vectors of $Q$ and $S$ are $10 \hat{ i }+15 \hat{ j }+20 \hat{ k }$ and $\alpha \hat{ i }+\beta \hat{ j }+\gamma \hat{ k }$ respectively, then which of the following is/are TRUE ?
Updated On: May 22, 2024
- $3(\alpha+\beta)=-101$
- $3(\beta+\gamma)=-71$
- $3(\gamma+\alpha)=-86$
- $3(\alpha+\beta+\gamma)=-121$
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The Correct Option is A, B, C
Solution and Explanation
(A) $3(\alpha+\beta)=-101$
(B) $3(\beta+\gamma)=-71$
(C) $3(\gamma+\alpha)=-86$
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