JEE Main On 08 April 2018 Question 26
Question: The length of the projection of the line segment joining the points (5, -1, 4) and (4, -1, 3) on the plane, $ x+y+z=7 $ is: [JEE Main Online 08-04-2018]
Options:
A) $ \frac{1}{3} $
B) $ \sqrt{\frac{2}{3}} $
C) $ \frac{2}{\sqrt{3}} $
D) $ \frac{2}{3} $
Show Answer
Answer:
Correct Answer: C
Solution:
Foot of perpendicular of point A on plane $ \frac{x-4}{1}=\frac{y-(-1)}{1}=\frac{z-3}{1}=-\frac{(-1)}{3} $
$ A(13/3,-2/3,10/3) $
Similarly, $ B(14/3,-4/3,11/3) $
$ AB=\sqrt{{{(14/3-13/3)}^{2}}+{{(-4/3+2/3)}^{2}}+{{(11/3-10/3)}^{2}}} $
$ =\sqrt{\frac{2}{3}} $
