A) \[\left( \frac{28}{9},\frac{83}{9},\frac{11}{9} \right)\]
B) \[(28,83,11)\]
C) \[(4,-3,4)\]
D) \[(2,-9,-1)\]
Correct Answer: D
Solution :
Given equation of line is \[\frac{x-2}{1}=\frac{y-1}{-2}=\frac{z-0}{2}=k\] [say] Any point on the line is \[Q(k+2,\,\,-2k+1,2k)\] Direction ratios of PQ are \[(k+2-6,-2k+1-3,2k-9)\] ie, \[(k-4,\,-2k-2,\,2k-9),\] Since, the line \[PQ\] is perpendicular to \[AB\]. \[\therefore \] \[1(k-4)-2(-2k-2)+2(2k-9)=0\] \[\Rightarrow \] \[k-4+4k+4+4k-18=0\] \[\Rightarrow \] \[9\,k=18\] \[\Rightarrow \] \[k=2\] \[\therefore \] Point Q is \[(4,-3,4)\]. Let the image of P about line AB is \[R({{x}_{1}},{{y}_{1}},{{z}_{1}}),\] Where Q is the mid point of PR. \[\therefore \] \[\frac{{{x}_{1}}+6}{2}=4,\,\frac{{{y}_{1}}+3}{2}=-3,\,\frac{{{z}_{1}}+9}{2}=4\] \[\Rightarrow \] \[{{x}_{1}}=2,\,{{y}_{1}}=-9,\,{{z}_{1}}=-1\]You need to login to perform this action.
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