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 o planes as \[(\hat{i}-\hat{j}+4\hat{k}).(\hat{i}+5\hat{j}+\hat{k})=0\] Any point on the given line is \[(\lambda +2,\,-\lambda -2,\,4\lambda +3).\] For \[\lambda =0\] a point on this line is \[(2,-2,3)\] and the distance from \[\vec{r}.(\hat{i}+5\hat{j}+\hat{k})=5\] or \[x+5y+z=5\] is \[d=\frac{|2+5(-2)+3-5|}{\sqrt{1+25+1}}=\frac{|-10|}{3\sqrt{3}}=\frac{10}{3\sqrt{3}}\]
You need to login to perform this action.
You will be redirected in
3 sec
