Question

Vector calculus problem

1. (3 pts) Suppose that two skew lines are described by Ri-ul + tv1 and R2 = u2+ tv2 Determine a formula for the distance between the lines in terms of ui,u2,v1 and v2, using scalar and vector products. (Skew lines do not intersect and are not parallel.)

Answer 1

"We know that short test distance will occur along the common normal to both lines and common normal will be along v^vector_1 times v^vector_2 thus short test distance will be = projection of AB on PN = (mu^vector_1 - mu^vector_2) PN^^ = (mu^vector_1 - mu^vector_2) (v^vector_1 times v^vector_2)/