Answer by TonyK for Find the shortest distance between two lines and their...
The line joining the two points $\vec x_1=\vec b_1 +s \vec r_1$ and $\vec x_2=\vec b_2 +t \vec r_2$ is parallel to$$\vec x_1-\vec x_2=\vec b_1-\vec b_2+s\vec r_1-t\vec r_2$$And if this is the shortest...
View ArticleAnswer by Andrei for Find the shortest distance between two lines and their...
Let's choose a point on $g_1$ and a point on $g_2$. The relative position of one point with respect to the other is $$\vec l(s,t) =(\vec b_2+t\vec r_2)-(\vec b_1+s\vec r_1)$$We say that the distance...
View ArticleAnswer by Peter Melech for Find the shortest distance between two lines and...
Decompose $\vec{F_{g_1}F_{g_2}}=\lambda_1\vec{r_1}+\lambda_2\vec{r_2}+\vec{v}$ where $\vec{v}\in\operatorname{span}\{\vec{r_1},\vec{r_2}\}^{\perp}$ then is it easy to see if $\vec{v}\neq \vec{0}$...
View ArticleFind the shortest distance between two lines and their coordinates.
$$g_1: \vec x = \vec b_1 +s \vec r_1, s, \in \mathbb{R}$$$$g_2: \vec x = \vec b_2 +t \vec r_2, t, \in \mathbb{R}$$Given this information calculate the values of $s$ and $t$. Using that find the...
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