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 ! }