question_answer

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]

A)  \[\frac{1}{3}\]                                   

B)  \[\sqrt{\frac{2}{3}}\]

C)  \[\frac{2}{\sqrt{3}}\]                        

D)  \[\frac{2}{3}\]

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, \[B(14/3,-4/3,11/3)\] \[AB=\sqrt{{{(14/3-13/3)}^{2}}+{{(-4/3+2/3)}^{2}}+{{(11/3-10/3)}^{2}}}\] \[=\sqrt{\frac{2}{3}}\]