How do i start this question? @mathmate

Let L1 be the line passing through the point P1=(3, 1, −3) with direction vector →d=[0, 1, 3]T, and let L2 be the line passing through the point P2=(−2, 1, −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.

Question

How do i start this question? @mathmate

Let L1 be the line passing through the point P1=(3, 1, −3) with direction vector →d=[0, 1, 3]T, and let L2 be the line passing through the point P2=(−2, 1, −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.

jim_thompson5910 · Answer

Here's how I visualize it

we have points P1 and P2 in 3space. Imagine we just focus on a plane that contains these two points, and the lines that run through them

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jim_thompson5910 · Answer

the lines point in the same direction. If we're restricted to this plane, then these lines are parallel

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