JEE Advanced 2022 Paper 1 Mathematics Q12

Mathematics

Problem

Let S be the reflection of a point Q with respect to the plane given by r⃗\vec{r}=−(t+p)î+tĵ+(1+p)k^\hat{k}, where t,p are real parameters and î,ĵ,k^\hat{k} are the unit vectors along the three positive coordinate axes. If the position vectors of Q and S are 10î+15ĵ+20k^\hat{k} and αî+βĵ+γk^\hat{k} respectively, then which of the following is/are TRUE?

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