Dot and cross products are tools from vector algebra — the dot product gives a scalar (like projecting one shadow on another) and cross product gives a vector perpendicular to both. For skew lines, you take vectors along each line, find a perpendicular vector via cross product, then project the vector connecting any point on line A to line B onto that perpendicular — that projection's magnitude is the shortest distance.
But yaar, I just used this in a Mumbai college mechanics lab to find the shortest distance between two misaligned shafts in a machine model. My real struggle was explaining it to my father on the phone, who laughed and said, "In our village, the shortest distance between two fields is a straight path, not these *cross-pross* vectors!
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