Question

For skew lines, which expression gives \[SD\]?

Options

• \[SD=\frac{|(\vec a_2-\vec a_1)\cdot(\vec b_1\times\vec b_2)|}{|\vec b_1\times\vec b_2|}\]

• \[SD=\frac{|\vec b_1\cdot\vec b_2|}{|\vec b_1\times\vec b_2|}\]

• \[SD=\frac{|(\vec a_2-\vec a_1)\times\vec b|}{|\vec b|}\]

• \[SD=\frac{|(\vec a_2-\vec a_1)\cdot\vec b_1|}{|\vec b_1|}\]

Answer 1

For skew lines, the shortest distance is obtained from a scalar triple product. The cross product \[\vec b_1\times\vec b_2\] supplies a direction perpendicular to both lines.