A) \[\frac{x+4}{0}=\frac{y-2}{0}=\frac{z-3}{1}\]
B) \[\frac{x-5}{0}=\frac{y-3}{0}=\frac{z}{1}\]
C) \[\frac{x}{0}=\frac{y}{0}=\frac{z-3}{1}\]
D) \[\frac{x}{1}=\frac{y}{1}=\frac{z-3}{0}\]
Correct Answer: C
Solution :
[c] Any point on the first line is \[P(-4+4\lambda ,\,2-2\lambda ,3)\]. Any point on the second line is \[Q(5+5\mu ,\,3+3\mu ,0)\] Both lines are perpendicular to z-axis. So, line PQ is parallel to z-axis. \[\therefore \,\,\,\,\,-4+4\lambda =5+5\mu \] and \[2-2\lambda =3+3\mu \] \[\Rightarrow \,\,\,\,\lambda =1,\,\,\mu =-1\] \[\therefore \,\,\,P(0,0,3)\] and \[Q(0,0,0)\]
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