Distance from a point to a line

本文探讨了从一点到直线的最短距离问题,利用勾股定理和向量方程来解决这一几何难题。首先,给出了通过点A和B的直线L的向量方程,接着计算了单位向量和从点C到直线L的垂直距离。

The problem

          Let 

                    and   

          be the position vectors of the points A, B and C respectively,         

          and L be the line passing through A and B.

 

          Find the shortest distance from C to L.

 

Method 1   By Pythagoras Theorem

 

          

          The vector equation of the line, L, which passes through A and B:

                  

                  

          A unit vector along AB :               

          

          Let D be the foot of the perpendicular from C to L. Then

                              

                  and          |AC| = Ö14

\The shortest distance from C to AB   = CD

                                                                          

                                                                          

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