A) \[\frac{10}{3\sqrt{3}}\]
B) \[\frac{10}{9}\]
C) \[\frac{10}{3}\]
D) \[\frac{3}{10}\]
Correct Answer: A
Solution :
[a] It is obvious that the given line and plane are parallel. Given point on the lie is \[A(2,-2,3).\] \[B(0,0,5)\] is a point the plane. Therefore, \[\xrightarrow[AB]{}=(2-0)\hat{i}+(-2-0)\hat{j}+(3-5)\hat{k}\] Then distance of B from the plane = Projection of \[\xrightarrow[AB]{}\]on vector \[\hat{i}+5\hat{j}+\hat{k}\] \[P=\left| \frac{(2\hat{i}-2\hat{j}-2\hat{k}).(\hat{i}+5\hat{j}+\hat{k})}{\sqrt{1+25+1}} \right|=\left| \frac{2-10-2}{\sqrt{27}} \right|=\frac{10}{3\sqrt{3}}\]You need to login to perform this action.
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