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 length of the projection of the line segment joining the pointsand on the plane $x+y+z=7$ is

1. A

$\sqrt{2/3}$

2. B

$\frac{\sqrt{2}}{3}$

3. C

$2/3$

4. D

$1/3$

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### Solution:

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

and  are   Let the angle between AB and plane is $\varphi$, which gives

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

The projection of AB on the plane

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

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