Let L₁ be the line passing through the point P₁=(2, −1, −1) with direction vector =[3, −3, −3]ª, and let L₂ be the line passing through the point P₂=(−2, −5, 1) with the same direction vector. Find the shortest distance d between these two lines, and find a point Q₁ on L₁ and a point Q₂ on L₂ so that d(Q1,Q₂) = ) = d. Use the square root symbol '' where needed to give an exact value for your answer.

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A: This is a question of 3D geometry and vector analysis.