Equation of plane is $$ \begin{aligned} & \vec{r}=-(t+p) \hat{i}+\hat{j}+(1+p) \hat{k} \\ & \vec{r}=\hat{k}+t(-\hat{i}+\hat{j})+p(-\hat{i}+\hat{k}) \end{aligned} $$ Equation of plane in standard form is $$ \begin{aligned} & {[\hat{r}-\hat{k}-\hat{i}+\hat{j}-\hat{i}+\hat{k}]=0} \\ & \therefore x+y+z=1 \end{aligned} $$ Coordinate of $Q=(10,15,20)$ Coordinate of $S=(\alpha, \beta, \gamma)$ $$ \begin{array}{ll} \therefore & \frac{\alpha-10}{1}=\frac{\beta-15}{1}=\frac{\gamma-20}{1}=\frac{-2(10+15+20-1)}{3} \\ \therefore & \alpha-10=\beta-15=\gamma-20=-\frac{88}{3} \\ \therefore & \alpha=-\frac{58}{3}, \beta=-\frac{43}{3}, \gamma=-\frac{28}{3} \end{array} $$
\begin{array}{ll} \therefore & 3(\alpha+\beta)=-101,3(\beta+\gamma)=-71 \\ & 3(\gamma+\alpha)=-86 \text { and } 3(\alpha+\beta+\gamma)=-129 \\ \therefore & \text { Ans. A, B, C } \end{array}