请制作一个本道题目的讲解视频---**Question Number:** 6 **Question Stem:** 如图，在三棱柱 ABC - A₁B₁C₁ 中，E,F 分别是 AB,AC 上的点，且 AE:EB = AF:FC，则 EF 与 B₁C₁ 的位置关系是 止 || B₁C₁. **Mathematical Formulas/Equations:** AE:EB = AF:FC **Chart/Diagram Description:** * **Type:** Three-dimensional geometric figure, specifically a triangular prism. * **Main Elements:** * **Vertices:** * Bottom base vertices: A (front-left), B (front-right), C (back-right). * Top base vertices: A₁ (directly above A), B₁ (directly above B), C₁ (directly above C). * **Edges:** * Vertical edges connecting the bases: AA₁, BB₁, CC₁. * Edges of the bottom base: AB, BC, AC (AC is shown as a dashed line, indicating it's a hidden edge). * Edges of the top base: A₁B₁, B₁C₁, A₁C₁. * **Points:** * E is a point located on the edge AB. * F is a point located on the edge AC. * **Lines/Segments:** * Segment EF is drawn, connecting points E and F. It is represented by a dashed line, implying it lies on a plane or is hidden from a certain perspective. * The problem refers to the relationship between segment EF and edge B₁C₁. * **Relative Position and Direction:** * The prism has a triangular base ABC at the bottom and A₁B₁C₁ at the top. * Points E and F are on the edges AB and AC, respectively, both belonging to the bottom face ABC. * Segment EF lies within the plane of the bottom base ABC. * Edge B₁C₁ is part of the top base A₁B₁C₁.