A line in 3-D is given by the parametric Vector
![\begin{displaymath}
{\bf v}=\left[{\matrix{x_0+at\cr y_0+bt\cr z_0+ct\cr}}\right].
\end{displaymath}](p2_809.gif) |
(1) |
The distance between a point on the line with parameter
and the point
is therefore
 |
(2) |
To minimize the distance, take
 |
(3) |
 |
(4) |
 |
(5) |
so the minimum distance is found by plugging (5) into (2) and taking the Square Root.
See also Line, Point, Point-Line Distance--2-D
© 1996-9 Eric W. Weisstein
1999-05-25