Step by Step solution about How to resolve the algorithm Find the intersection of a line with a plane step by step in the Mathematica / Wolfram Language programming language

Wolfram Programming Language:

The Wolfram Programming Language (WPL) is a technical computing language developed by Wolfram Research. It is designed for symbolic and numeric computation, data analysis, visualization, and more.

Explanation of the Source Code:

The provided WPL code calculates the intersection of an infinite line and an infinite plane. Here's how it works:

1. Infinite Line:

InfiniteLine[{0, 0, 10}, {0, -1, -1}]

This creates an infinite line passing through the point (0, 0, 10) and having a direction vector (0, -1, -1).

2. Infinite Plane:

InfinitePlane[{0, 0, 5}, {{0, 1, 0}, {1, 0, 0}}]

This creates an infinite plane passing through the point (0, 0, 5) with two normal vectors (0, 1, 0) and (1, 0, 0).

3. Region Intersection:

RegionIntersection[InfiniteLine[...], InfinitePlane[...]]

The RegionIntersection function is used to calculate the intersection of the infinite line and the infinite plane. The result is a geometric object that represents the intersection region.

Output:

The output of the code is a point, which is the intersection of the infinite line and the infinite plane. In this case, the intersection is:

{(5, 5, 5)}

Note:

This example demonstrates the use of WPL to perform geometric computations. WPL provides a powerful set of functions for working with geometric objects and performing various mathematical operations.

RegionIntersection[InfiniteLine[{0, 0, 10}, {0, -1, -1}], InfinitePlane[{0, 0, 5}, {{0, 1, 0}, {1, 0, 0}}]]