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

Answer: (B)

5

Answer 2

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): $5$