JEE Main & Advanced
JEE Main Paper (Held on 08-4-2019 Morning)
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.