3d Geometry

Step 1: Identifying direction vector and point.
For both lines, the direction vector is .

Step 2: Finding the difference vector.
The difference between a point on line 1 and a point on line 2 is:

Step 3: Using the shortest distance formula.
For parallel lines, the shortest distance is given by: Here, and . Now calculate the dot product and magnitude to find the distance.

Step 1: Understanding the formula.
The shortest distance between two skew lines is given by the formula: where: - and are points on lines 1 and 2 respectively, - and are direction vectors of the two lines.

Step 2: Finding the direction vectors.
For line 1: For line 2:

Step 3: Finding the difference vector.
The difference vector between a point on line 1 and a point on line 2 is:

Step 4: Calculate the cross product.
Now, compute and substitute the values into the formula for the shortest distance.

Step 5: Conclusion.
Once the cross product and dot product are calculated, substitute the values into the distance formula to get the shortest distance.