how do you prove that the shortest distance from a point to a line ($\displaystyle L$) in $\displaystyle R^3$ (or any $\displaystyle R^n$) is achieved along the perpendicular line connecting A to line($\displaystyle L$).
thanks
how do you prove that the shortest distance from a point to a line ($\displaystyle L$) in $\displaystyle R^3$ (or any $\displaystyle R^n$) is achieved along the perpendicular line connecting A to line($\displaystyle L$).
thanks
On the assumption that a unique perpendicular $\displaystyle RP$ from point $\displaystyle R$ of line $\displaystyle L$ to point $\displaystyle P$ always exists, you may consider $\displaystyle \bigtriangleup PQR$, where $\displaystyle
Q$ is any other point on line $\displaystyle L$.