Suppose that $A(0,0,0), B(1,2,0), C(0,-3,2)$ and $D(3,-4,5)$ and $AB, AC$ and $AD$ are three edges of a parallelepiped.

If $l_1$ is the line passing through $A$ and $B$ and $l_2$ is the line passing through $D$ and parallel to $AC$, then the distance between the skew lines $l_1$ and $l_2$ is the height of the parallelepiped.

The statement above is extracted from a solution set.

Question: Why the height is the distance between $l_1$ and $l_2$? I thought it should be $\| \vec{AD} \|$?


See the following picture:

enter image description here

Since it is a parallelepiped, not a rectangular box, the height is apparently not $||AD||$. It should be $||DH||$, which is the distance between the two lines.


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