A) \[10\sqrt{3}\]
B) \[5\sqrt{3}\]
C) \[3\sqrt{10}\]
D) \[3\sqrt{5}\]
Correct Answer: A
Solution :
Line through P(1, - 5, 9) parallel to x = y = z is \[\frac{x-1}{1}=\frac{y+5}{1}=\frac{z-9}{1}=\lambda (say)\] \[Q(x=1+\lambda ,y=-5+\lambda ,z=9+\lambda )\] Given plane \[x-y+z=5\] \[\therefore \]\[1+\lambda +5-\lambda +9+\lambda =5\] \[\Rightarrow \]\[\lambda =-10\] \[\therefore \]\[Q(-9,-15,-1)\] \[\therefore \]\[PQ=\sqrt{{{(1+9)}^{2}}+{{(15-5)}^{2}}+{{(9+1)}^{2}}}\] \[=\sqrt{300}=10\sqrt{3}\]
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