For the life of me; this whole topic makes no sense at all !
The parametric vector form of the line L1 is given as r1 = u1 + rv1 ( is a real number)
where 1 u is the position vector of 1 P1 = (1,1,−3) and v1 = P1P2where P2 = (3,3,−2) .
The parametric vector form of the line L2 is given as r2 = u2 + sv2 (s is a real number)
where u2 is the position vector of P3 = (−2,0,2) and v2 = −j− k .
(a) Give the parametric scalar equations of the lines L1 and L2
(b) Find the unit vector ˆn with negative i component which is perpendicular to both L1and L2
(c) The shortest distance between two lines is the length of a vector that connects the two lines and is perpendicular to both lines. For L1 and L2
this is expressed in the vector equation r2 −r1 = tnˆ where (t is a real number) is a
parameter. Write this equation as 3 scalar equations and hence obtain a system of three linear equations for the three parameters r, s and t .
(d) Solve this system of equations for r, s and t and hence find the shortest distance between the two lines L2 and L2
(e) Find the point Q on line L1 which is closest to line L2
Thanks for any help !