I would like to ask if it's possible to calculate the shortest distance in space between a point and a straight line in a more unusual or complicated way. For example, we have a point $A=(1,2,3)$ and a straight line with this parametric equation:
$$x = t+1; y = 2t; z = t-1;$$
Is it possible to find the shortest distance from $A$ to the line by considering a point $H=(t+1,2t,t-1)$, the center of the sphere and $AH$ the radius of the sphere? Or find the symmetry of $A$ with respect to the line and find their midpoint $H$?