[size=100]Let [math]A=\left(0,0,0\right),[/math] [math]B=\left(9,8,12\right),[/math] and [math]C=\left(6,2,3\right).[/math] Find coordinates for the point line [math]AB[/math] that is closest to [math]C.[/math][/size][br][br]Suppose we call this closest point [math]P.[/math] We know that segment [math]CP[/math] must be perpendicular to line [math]AB.[/math] But that means [math]\overrightarrow{AP}[/math] is the projection of [math]\overrightarrow{AC}[/math] onto [math]\overrightarrow{AB}[/math].[br][br]Try computing this projection to find the coordinates of [math]P.[/math][br] [br]