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