MathDB

Consider positive numbers

d,v

such that

d>v

. Moreover, consider two perpendicular skew lines

p,q

of distance

v

(that is direction vectors of both lines are orthogonal and

\min_{X\in p,Y\in q}XY = v

). Finally, consider all line segments

PQ

such that

P\in p, Q\in q, PQ=d

. a) Find the locus of all points

P

. b) Find the locus of all midpoints of segments

PQ

Problem Statement