Mathematics · supplementary
Shortest distance between parallel lines in direction-ratio form for JEE
Equation of a line; Skew lines, the shortest distance between them and its equation
Formula
\(d=\frac{\sqrt{|\vec{PQ}|^2(a^2+b^2+c^2)-\big((x_2-x_1)a+(y_2-y_1)b+(z_2-z_1)c\big)^2}}{\sqrt{a^2+b^2+c^2}}\)
Variables: Parallel lines have common direction ratios \((a,b,c)\); \(P(x_1,y_1,z_1)\), \(Q(x_2,y_2,z_2)\) are points on them; \(|\vec{PQ}|^2=(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2\).
Coordinate computation of distance between parallel lines.