The coordinates at the two ends of a certain length dimension have been measured by a CMM$.$ The coordinates of the first end are $(120\mathrm{.}5,50\mathrm{.}2,20\mathrm{.}2),$ and the coordinates of the opposite end are $(23\mathrm{.}1,11\mathrm{.}9,20\mathrm{.}3),$ where the units are mm$.$ The given coordinates have been corrected for probe radius. Determine the length dimension that would be computed by the CMM software.

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Three point locations on the surface of a cylinder have been measured by a coordinate measuring machine. The cylinder is positioned so that its axis is perpendicular to the x$-$y plane. The three coordinates in the x$-$y axes are: $(5\mathrm{.}242,0\mathrm{.}124),(0\mathrm{.}325,4\mathrm{.}811),$ and $(4\mathrm{.}073,0\mathrm{.}544),$ where the units are inches. The coordinates have been corrected for probe radius. Determine $($a$)$ the coordinates of the cylinder axis and $($b$)$ the cylinder diameter, as they would be computed by the CMM software.

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Three point locations on the flat surface of a part have been measured by a CMM$.$ The three point locations are $(225\mathrm{.}21,150\mathrm{.}23,40\mathrm{.}17),(14\mathrm{.}24,140\mathrm{.}92,38\mathrm{.}29),$ and $(12\mathrm{.}56,22\mathrm{.}75,38\mathrm{.}02),$ where the units are mm$.$ The coordinates have been corrected for probe radius. $($a$)$ Determine the equation for the plane in the form of Equation x $+$ A y $+$ B z $+$ C $=0.$