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?
