Let L ₁  be the line passing through the point P ₁  =(−3, −2, −2) with direction vector →d=[0, 2, 3] ^T  , and let L ₂  be the line passing through the point P ₂  =(5, 4, −4) with the same direction vector. 

 

Find the shortest distance d between these two lines, and find a point Q ₁  on L ₁  and a point Q ₂  on L ₂  so that d(Q ₁  ,Q ₂  ) = d.  Use the square root symbol '√' where needed to give an exact value for your answer. 

 

  d =  0 

 

  Q ₁  = (  0   ,   0   ,   0   ) 

Q ₂  = (  0   ,   0   ,   0   )