A) \[(2,-4,-7)\]
B) \[(2,4,7)\]
C) \[(2,-4,7)\]
D) \[(-2,4,7)\]
Correct Answer: A
Solution :
Let\[{{L}_{1}}\equiv \frac{x-3}{1}=\frac{y+1}{3}=\frac{z-6}{-1}=\alpha \] and\[{{L}_{2}}\equiv \frac{x+5}{7}=\frac{y-2}{-6}=\frac{z-3}{4}=\beta \] \[\therefore \]Point on \[{{L}_{1}}\] is \[(\alpha +3,3\alpha -1,-\alpha +6)\]and point on\[{{L}_{2}}\]is\[(7\beta -5,-6\beta +2,4\beta +3)\] As the lines \[{{L}_{1}}\]and \[{{L}_{2}}\]intersect at R. \[\therefore \]\[\alpha +3=7\beta -5,3\alpha -1=-6\beta +2\] \[\Rightarrow \]\[\alpha -7\beta =-8\] ?(i) and\[3\alpha +6\beta =3\Rightarrow \alpha +2\beta =1\] ...(ii) \[\therefore \]Solving (i) and (ii), we get \[\alpha =-1,\beta =1\] \[\therefore \]Co-ordinates of point R is (\[2,-4,7\]). \[\therefore \]Reflection of point R in the xy-plane is (\[2,-4,-7\]).
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