# Distance Between Two Skew Lines Calculator

**Introduction**

Calculating the distance between two skew lines is a crucial task in geometry, helping us understand the spatial relationship between non-intersecting lines in three-dimensional space. In this article, we will provide a user-friendly HTML and JavaScript code for a distance calculator using the most accurate formula. This calculator will empower users to effortlessly determine the distance between two skew lines.

**How to Use**

To use the Distance Between Two Skew Lines Calculator, follow these simple steps:

- Enter the coordinates of a point on the first line.
- Specify the direction vector of the first line.
- Enter the coordinates of a point on the second line.
- Specify the direction vector of the second line.
- Click the “Calculate” button to obtain the distance between the two skew lines.

**Formula**

The formula for calculating the distance (d) between two skew lines represented by the vectors $r $ and $r $ is given by:

$d=d ×d ∣(r −r )⋅(r ×d ×d )∣ $

Where:

- $r $ and $r $ are position vectors on the lines.
- $d $ and $d $ are direction vectors of the lines.

**Example**

Let’s consider two skew lines with the following information:

Line 1:

- Point: $P_{1}(1,2,3)$
- Direction Vector: $d =⟨2,−1,3⟩$

Line 2:

- Point: $P_{2}(4,5,6)$
- Direction Vector: $d =⟨−1,2,1⟩$

Using the formula, we find the distance: $d=(,,)∣(,,)⋅(,,)∣ =155 54 $

**FAQs**

**Q1: Are skew lines always non-intersecting? **

A1: Yes, skew lines do not intersect and are always non-coplanar.

**Q2: Can this calculator be used for lines in any orientation? **

A2: Yes, the calculator accommodates lines in any orientation in three-dimensional space.

**Q3: Is there a limit to the number of decimal places in the result?**

A3: The calculator provides a precise result with as many decimal places as necessary.

**Conclusion**

In conclusion, our Distance Between Two Skew Lines Calculator provides an efficient solution for determining the spatial separation of non-intersecting lines. The HTML and JavaScript code presented here ensures a user-friendly experience, allowing individuals to effortlessly perform these geometric calculations.