3D Vector Line Intersections

① This example demonstrates the intersection of two vector-parameterized lines in 3D space, using interactive buttons and sliders to visualize the geometric condition for lines to meet. ② Core mathematical concepts include vector equations of lines, parametric representation, direction vectors, existence of intersection points, and solving linear systems in three dimensions. ③ Construction highlights: the Vector command defines direction vectors u and w, Line constructs the lines L_1 and another line, Slope may assist in computing direction ratios; objects include points A, B, D, E, F, G, H, parameters t and s, buttons button1 and button2 for stepwise or toggle display, and text objects text2–text6 for labeling coordinates and equations. ④ Suitable for senior high school or early university students learning spatial analytic geometry and vector algebra, as well as for teachers demonstrating dynamic 3D line intersection in class.