question_answer

The length of the perpendicular from the point (2, -1, 4) on the straight line,\[\frac{x+3}{10}=\frac{y-2}{-7}=\frac{z}{1}\]is: [JEE Main 8-4-2019 Morning]

A) less than 2

B) greater than 3 but less than 4

C) greater than 4

D) greater than 2 but less than 3

Correct Answer: B

Solution :

Now,\[\overrightarrow{MP}.\left( 10\hat{i}-7\hat{j}+\hat{k} \right)=0\]\[\Rightarrow \]\[\lambda =\frac{1}{2}\] \[\therefore \] Length of perpendicular \[(=PM)=\sqrt{0+\frac{1}{4}+\frac{49}{4}}\] \[=\sqrt{\frac{50}{4}}=\sqrt{\frac{25}{2}}=\frac{5}{\sqrt{2}},\] which is greater than 3 but less than 4.