Three Dimensional Geometry

Concept: The shortest distance between two skew lines in 3D space is the length of the perpendicular between them. If the lines are: Then the shortest distance is given by: Step 1: Identify components.
From the given vector equations: \begin{itemize} \item = position vectors of points on each line \item = direction vectors of the lines \end{itemize}
Step 2: Find vector joining the points.

Step 3: Find cross product of direction vectors.
This gives a vector perpendicular to both lines.
Step 4: Use scalar triple product.


Step 5: Divide by magnitude of cross product.
Conclusion:
Use the above formula by substituting the given vectors to obtain the shortest distance.