question_answer

The distance of the point having position vector \[-\hat{i}+2\hat{j}+6\hat{k}\] from the straight line passing through the point (2, 3, -4) and parallel to the vector, \[6\hat{i}+3\hat{j}-4\hat{k}\]is: [JEE Main 10-4-2019 Afternoon]

A) \[7\]     

B) \[4\sqrt{3}\]

C) \[2\sqrt{13}\]              

D) 6

Correct Answer: A

Solution :

\[AD=\left| \frac{\overrightarrow{AP}.\vec{n}}{|\vec{n}|} \right|=\sqrt{61}\] \[\Rightarrow PD=\sqrt{A{{P}^{2}}-A{{D}^{2}}}=\sqrt{110-61}=7\]