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is given as r1 = u1 + rv1 (r element of real field)

where u1 is the position vector of P1 = (1,1,−3) and v1=vectorP1P2

where

P2 = (3,3,−2) .

The parametric vector form of the line 2

is given as r2 = u2 + sv2 (s element of real field)

where 2 u 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 l1

and 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 2 1

r −r = tnˆ where t element of real field 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 1

and 2

.

(e) Find the point Q on line 1

which is closest to line 2

I've done bits and pieces of the question bu i'm especially stuck on parts c d and e. please help thank you