Two lines x−31=y+13=z−6−1 and x+57=y−2−6=z−34 intersect at the point R. The reflection of R in the xy-plane has coordinates :-

Point on L1(λ+3,3λ−1,−λ+6)Point on L2(7μ−5,−6μ+2,4μ+3) ⇒λ+3=7μ−5 3λ−1=−6μ+2 …. (1)Point on (2,−4,7) …. (2) ⇒λ=−1,μ=1Reflection is (2,−4,−7)

Two lines x−31=y+13=z−6−1 and x+57=y−2−6=z−34 intersect at the point R. The reflection of R in the xy-plane has coordinates :-

Point on L1(λ+3,3λ−1,−λ+6)Point on L2(7μ−5,−6μ+2,4μ+3) ⇒λ+3=7μ−5 3λ−1=−6μ+2 …. (1)Point on (2,−4,7) …. (2) ⇒λ=−1,μ=1Reflection is (2,−4,−7)

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Two lines $\frac{x - 3}{1} = \frac{y + 1}{3} = \frac{z - 6}{- 1}$ and $\frac{x + 5}{7} = \frac{y - 2}{- 6} = \frac{z - 3}{4}$ intersect at the point R. The reflection of R in the xy-plane has coordinates :-

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$(2, 4, 7)$

$(- 2, 4, 7)$

$(2, - 4, - 7)$

$(2, - 4, 7)$

answer is C.

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Detailed Solution

Point on $L_{1} (λ + 3, 3 λ - 1, - λ + 6)$
Point on $L_{2} (7 μ - 5, - 6 μ + 2, 4 μ + 3)$
$\Rightarrow λ + 3 = 7 μ - 5$
$3 λ - 1 = - 6 μ + 2$ …. (1)
Point on $(2, - 4, 7)$ …. (2)
$\Rightarrow λ = - 1, μ = 1$
Reflection is $(2, - 4, - 7)$