Question

Let \(Q\) be the mirror image of the point \(P(1, 0, 1)\) with respect to the plane \(S\): \(x + y + z = 5\). If a line L passing through \((1, –1, –1)\), parallel to the line \(PQ\) meets the plane \(S\) at \(R\), then \(QR_2\) is equal to :

• A. 2
• B. 5
• C. 7
• D. 11

Answer 1

The Correct Option is B

Since \(L\) is parallel to \(PQ\) d.r.s of \(S\) is \((1, 1, 1)\)
\(L=\frac {x−1}{1}=\frac {y+1}{1}=\frac {z+1}{1}\)
Point of intersection of \(L\) and \(S\) be \(λ\)
\((λ + 1) + (λ – 1) + (λ – 1) = S\)
\(λ = 2\)
\(R= (3, 1, 1)\)
Let \(Q (α, β, γ)\)
\(\frac {α−1}{1}=\frac β1=\frac {γ−1}{1}=−\frac {2(3)}{3}\)
\(α = 3\)
\(β = 2\)
\(γ = 3\)
\(Q≡ (3, 2, 3)\)
\((QR)^2 = 0^2 + (1)^2 + (2)^2 = 5\)
\((QR)^2 = 5\)

So, the correct option is (B): \(5\)