A) \[\sqrt{29}\]
B) \[\sqrt{33}\]
C) \[\sqrt{53}\]
D) \[\sqrt{66}\]
Correct Answer: C
Solution :
Let feet of perpendicular is \[(2\alpha ,3\alpha +2,4\alpha +3)\] \[\Rightarrow \]D' ratio of the \[\bot \] line \[<2\alpha -3,3\alpha +3,3\alpha +3,4\alpha -8>\]and D' ratio of the line < 2, 3, 4 > \[\Rightarrow \]\[2(2\alpha -3)+3(3\alpha +3)+4(4\alpha -8)=0\] \[\Rightarrow \]\[29\alpha -29=0\] \[\Rightarrow \]\[\alpha =1\] \[\Rightarrow \]feet of \[\bot \]is (2, 5, 7) \[\Rightarrow \]length \[\bot \]is \[\sqrt{{{1}^{2}}+{{6}^{2}}+{{4}^{2}}}\] \[=\sqrt{53}\]
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