Mathematics · essential
Shortest distance between two skew lines in determinant form for JEE
Equation of a line; Skew lines, the shortest distance between them and its equation
Formula
\(d=\frac{\left|\begin{vmatrix}x_2-x_1 & y_2-y_1 & z_2-z_1\\ a_1 & b_1 & c_1\\ a_2 & b_2 & c_2\end{vmatrix}\right|}{\sqrt{(b_1c_2-b_2c_1)^2+(c_1a_2-c_2a_1)^2+(a_1b_2-a_2b_1)^2}}\)
Variables: Lines pass through \((x_1,y_1,z_1)\), \((x_2,y_2,z_2)\) and have direction ratios \((a_1,b_1,c_1)\), \((a_2,b_2,c_2)\).
Conditions: Lines are non-parallel.
Coordinate form of shortest distance between skew lines.