Shortest Distance Between Two Lines Using Determinant

Shortest Distance Between Two Lines Using Determinant

If the direction ratios of two lines are:

$$a_1:b_1:c_1$$

and:

$$a_2:b_2:c_2$$

and points on them are:

$$P_1(x_1,y_1,z_1)$$

and:

$$P_2(x_2,y_2,z_2)$$

then:

$$d=\frac{|(\vec P_1\vec P_2)\cdot(\vec d_1\times\vec d_2)|}{|\vec d_1\times\vec d_2|}$$

Usage

- Used for shortest-distance problems when line directions and points are given.