The New Right: Right-Hand Rule in 3D Vectors | 新右手系：三维向量中的右手定则

📚 The New Right: Right-Hand Rule in 3D Vectors | 新右手系：三维向量中的右手定则

In Edexcel A-Level Mathematics, the phrase “the new right” is a playful reminder of the right-hand rule used to describe orientation in three-dimensional coordinate systems and vector cross products. This revision note covers the key concepts, formulas and exam techniques you need for 3D vectors.

在 Edexcel A-Level 数学中，“新右手系”这一说法是对三维坐标系和向量叉积中右手定则的形象提醒。本文复习 3D 向量所需的关键概念、公式和考试技巧。

1. Introduction to 3D Coordinate Systems | 三维坐标系简介

A three-dimensional coordinate system uses three mutually perpendicular axes, usually labelled x, y and z. Points in space are described by ordered triples (x, y, z), and every vector can be represented by its components along these axes. The orientation of the axes can be either right-handed or left-handed, and the choice affects the signs of cross products.

三维坐标系使用三条互相垂直的坐标轴，通常标记为 x、y 和 z。空间中的点用有序三元组 (x, y, z) 表示，每个向量都可以用沿这些轴的分量来表示。坐标轴的取向可以是右手系或左手系，这一选择会影响叉积的符号。

In Edexcel exams, you will mostly work with Cartesian coordinates in three dimensions. Understanding the spatial arrangement of the axes is essential before moving on to vector operations such as the scalar product and the cross product.

在 Edexcel 考试中，你主要接触的是三维笛卡尔坐标。在进行标量积和叉积等向量运算之前，理解坐标轴的空间排列是至关重要的。

2. The Right-Hand Coordinate System | 右手坐标系

In a right-handed system, if you point your right thumb along the positive x-axis and your index finger along the positive y-axis, your middle finger points along the positive z-axis. This is the standard convention used in mathematics, physics and most Edexcel mechanics problems.

在右手坐标系中，如果你将右手拇指指向正 x 轴，食指指向正 y 轴，那么中指就指向正 z 轴。这是数学、物理以及大多数 Edexcel 力学问题中使用的标准约定。

Edexcel examinations always assume a right-handed coordinate system unless stated otherwise. When you draw 3D diagrams, it is helpful to sketch the axes consistently: x to the right, y into the page or upwards, and z upwards or outwards, depending on the convention you use.

除非另有说明，Edexcel 考试始终默认使用右手坐标系。绘制三维图时，保持坐标轴方向一致会很有帮助：通常 x 轴向右，y 轴向内或向上，z 轴向上或向外，具体取决于你所采用的惯例。

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