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  4. Two lines (x-3/1) = (y+1/3) = (z-6/-1) and (x+5/7) = (y-2/-6) = (z-3/4) intersect at the point R. The reflection of R in the xy-plane has coordinates :

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Q. 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 :

JEE MainJEE Main 2019Three Dimensional Geometry

Solution:

Point on $L_1 (\lambda + 3, 3\lambda - 1, - \lambda + 6)$
Point on $L_2 (7 \mu - 5, - 6 \mu + 2, 4\mu + 3)$
$\Rightarrow \; \lambda + 3 = 7 \mu - 5$ ...(i)
$3 \lambda - 1 = - 6 \mu + 2 $ ...(ii)
$\Rightarrow \; \lambda = -1, \mu = 1$
point $R(2,-4,7)$
Reflection is $(2,-4,-7)$