Question

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 \(\alpha\hat{i}+\beta{\hat{j} +γ\hat{k}}\) respectively, then which of the following is/are

(A) 3(α +β) = 101

(B) 3(β+γ) = -71

(C) 3(γ+α) = -86

(D) 3(α+β+γ) = -121

Answer 1

(A) 3(α +β) = 101

(B) 3(β+γ) = -71

(C) 3(γ+α) = -86

Clearly plane is given by x + y + z = 1 

using mirror image formula