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 points `(

1.	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
Answer» `A(5,-1,4) and B(4,-1,3)` `AB=(4-5)veci + (-1+1)vecj + (3-4)veck` `=-veci-veck` `abs(AB)=sqrt2` `x+y+z=7` `n=(veci+vecj+veck)` Equation of plane `vecrvecn=d` `(xveci+yvecj+zveck)(veci+vecj+veck)=7` `absn=sqrt3` `P=ABsintheta` `costheta =(vec(AB)vecn)/(abs(AB)absvecn)` `=((-veci-veck)(veci+vecj+veck))/(sqrt2sqrt3)` `=costheta=-sqrt2/sqrt3` `sintheta=sqrt(1-cos^2theta)` `sintheta=1/sqrt3` `P=sqrt21/sqrt3=sqrt2/sqrt3`

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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

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