Mathematics · essential
Coplanarity condition for two lines for JEE
Equation of a line; Skew lines, the shortest distance between them and its equation
Formula
\(\begin{vmatrix}x_2-x_1 & y_2-y_1 & z_2-z_1\\ a_1 & b_1 & c_1\\ a_2 & b_2 & c_2\end{vmatrix}=0\)
Variables: Lines are \(\vec r=\vec r_1+\lambda(a_1,b_1,c_1)\) and \(\vec r=\vec r_2+\mu(a_2,b_2,c_2)\); points \((x_1,y_1,z_1)\), \((x_2,y_2,z_2)\) lie on them respectively.
Testing whether two non-parallel lines intersect or are skew.