A) 3
B) \[\sqrt{11}\]
C) \[\sqrt{13}\]
D) 5
Correct Answer: C
Solution :
Given, line \[\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\] \[\Rightarrow \] \[\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}=\lambda \] (say) \[\Rightarrow \] \[x=\lambda ,y=2\lambda +1,z=3y+2\] Therefore, direction ratios of PQ are \[\lambda -1,2\lambda +1-6,3\lambda +2-3\] \[\Rightarrow \] \[\lambda -1,2\lambda -5,3\lambda -1\] \[\because \] PQ is perpendicular to the given line. Therefore, \[1(\lambda -1)+2(2\lambda -5)+3(3\lambda -1)=0\] \[\Rightarrow \] \[\lambda =1\] \[\therefore \] The coordinate of Q (1, 3, 5). \[\therefore \]Length of perpendicular \[=\sqrt{{{(1-1)}^{2}}+{{(3-6)}^{2}}+{{(5-3)}^{2}}}\] \[=\sqrt{9+4}=\sqrt{13}.\]You need to login to perform this action.
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