Final answer:
To find the distance between two skew lines, you can use the formula d = |(x₂ - x₁) - [(x₂ - x₁) . (u₁ x u₂)](u₁ x u₂)|. The equation involves the direction vectors of the two lines and uses dot and cross products.
Step-by-step explanation:
To find the distance between two skew lines, we need to find the shortest distance between any two points on each line. We can achieve this by finding the perpendicular distance from a point on one line to the other line. Let's consider a point on the first line with coordinates (x₁, y₁, z₁) and a point on the second line with coordinates (x₂, y₂, z₂). The distance between the two lines is given by the formula:
d = |(x₂ - x₁) - [(x₂ - x₁) . (u₁ x u₂)](u₁ x u₂)|,
Where u₁ and u₂ are the direction vectors of the two lines, and . denotes the dot product and x denotes the cross product.