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How do we find the shortest distance between two parallel lines? Two parallel lines will never intersect; The shortest distance between two parallel lines will be the perpendicular distance between them; Given a line with equation and a line with equation then the shortest distance between them can be found using the following steps:
The formula for the shortest distance between two points or lines whose coordinate are (x 1 y 1), and (x 2, y 2) is: \(\sqrt{(x 2-x 1)^2+(y 2-y 1)^2}\). This formula is also known as the distance formula.
27 sty 2023 · For the two non-intersecting lines which lie in the same plane, the shortest distance between them is the shortest distance between two points on the lines. We will learn more about the shortest distance between the two lines in this article.
Derive formulas to find the shortest distance between two lines. Learn about the equation of a line of the shortest distance between two lines at BYJU’S to clear IIT JEE Main and Advanced.
The distance between two points on $L$ and $M$ is $D =(a+bt-c-ds)^2 =(e+bt-ds)^2 $ where $e = a-c$. For this to be a minimum, taking partials, we want $D_s = D_t = 0$. $D_s = -2d(e+bt-ds) $ and $D_t = 2b(e+bt-ds) $. Therefore, with multiplication of vectors being dot product, $0 =d(e+bt-ds) =de+dbt-d^2s $ and $0 =b(e+bt-ds) =be+b^2t-bds) $.
The shortest distance from any point to a line will always be the perpendicular distance. Given a line l with equation and a point P not on l. The scalar product of the direction vector, b, and the vector in the direction of the shortest distance will be zero.
4 paź 2022 · $\begingroup$ Shortest distance is perpendicular to both lines. That's why it is perpendicular to $n_1\times n_2$ and $n_3\times n_4$, where $n_1(1,-1,1)$, $n_2(2,-3,4)$, $n_3(1,1,2)$, $n_4(2,3,3)$ (coefficients for line equations). $n_1\times n_2=n_5(-1,-2,-1)$, $n_3\times n_4=n_6(-3,1,1)$.
