For the life of me; this whole topic makes no sense at all !
The parametric vector form of the line L_{1} is given as r_{1} = u1 + rv1 ( is a real number)
where 1 u is the position vector of 1 P_{1} = (1,1,−3) and v_{1} = P_{1}P_{2}where P_{2} = (3,3,−2) .
The parametric vector form of the line L_{2} is given as r_{2} = u_{2} + sv_{2} (s is a real number)
where u_{2} is the position vector of P_{3} = (−2,0,2) and v_{2} = −j− k .
(a) Give the parametric scalar equations of the lines L_{1} and L_{2}
(b) Find the unit vector ˆn with negative i component which is perpendicular to both L_{1}and L_{2}
(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 L_{1} and L_{2}
this is expressed in the vector equation r_{2} −r_{1} = 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 L_{2 }and L_{2}
(e) Find the point Q on line L_{1} which is closest to line L_{2 Thanks for any help ! }