Problem
Let S be the reflection of a point Q with respect to the plane given by r = −(t + p)i + tj + (1 + p)k where t, p are real parameters and i, j, k are the unit vectors along the three positive coordinate axes. If the position vectors of Q and S are 10i + 15j + 20k and αi + βj + γk respectively, then which of the following is / are TRUE?
A 3(α + β) = −101
B 3(β + γ) = −71
C 3(γ + α) = −86
D 3(α + β + γ) = −121