A) \[\frac{10}{9}\]
B) \[\frac{10}{3\sqrt{3}}\]
C) \[\frac{3}{10}\]
D) \[\frac{10}{3}\]
Correct Answer: C
Solution :
Here, \[(\hat{i}-\hat{j}+4\hat{k}).(\hat{i}+5\hat{j}+\hat{k})=0\] So, the equation of the line parallel to the plane is The general point on this line is\[(\lambda +2,-\lambda -2,4\lambda +3)\]for\[\lambda =0\]the point on the line is and distance from \[\overrightarrow{r}.(\hat{i}+5\hat{j}+\hat{k})=5\]or\[x+5y+z=5\] \[\therefore \] \[d=\left| \frac{2+5(-2)+3-5}{\sqrt{1+25+1}} \right|\] \[\Rightarrow \] \[d=\left| \frac{-10}{3\sqrt{3}} \right|=\frac{10}{3\sqrt{3}}\]
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