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

The direction ratios of AB, where $A (5, - 1, 4)$

and $B (4, - 1, 3)$ are $(1, 0, 1)$ Let the angle between AB and plane is $ϕ$ , which gives

$\sin \emptyset = \frac{2}{\sqrt{6}}$ is $\cos \emptyset = \frac{1}{\sqrt{3}}$

The projection of AB on the plane $= A B \cos \emptyset$

$= \sqrt{2}$ . $\frac{1}{\sqrt{3}}$ $= \sqrt{\frac{2}{3}}$

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