Vectors: A Complete Guide for IGCSE Edexcel Mathematics | 向量：IGCSE Edexcel 数学完全指南

📚 Vectors: A Complete Guide for IGCSE Edexcel Mathematics | 向量：IGCSE Edexcel 数学完全指南

In the Edexcel IGCSE Mathematics syllabus, vectors are a key topic that combines abstract reasoning with practical applications. This guide will walk you through every essential concept you need for your exams.

在爱德思 IGCSE 数学考试大纲中，向量是一个将抽象推理与实际应用相结合的关键主题。本指南将带你逐项掌握考试所需的每一个核心概念。

1. Scalars and Vectors | 标量与向量

A scalar is a quantity that has only magnitude, or size. Examples include mass, time, temperature and speed.

标量是只有大小的量，例如质量、时间、温度或速率。

A vector is a quantity that has both magnitude and direction. Examples include displacement, velocity and acceleration.

向量是既有大小又有方向的量，例如位移、速度和加速度。

• Mass is a scalar: it has no direction.
  质量是标量：没有方向。
• Displacement is a vector: it describes both how far and in which direction.
  位移是向量：它同时描述距离和方向。

2. Representing Vectors | 向量的表示

A vector can be represented by a directed line segment. The length of the segment shows its magnitude, and the arrow shows its direction.

向量可以用有向线段表示。线段的长度表示它的大小，箭头表示它的方向。

In column form, a vector with components x and y is written as (x, y). For example, the vector 2i + 3j can be written as (2, 3).

在列向量形式中，具有分量 x 和 y 的向量写为 (x, y)。例如，向量 2i + 3j 可以写为 (2, 3)。

The letters i and j denote unit vectors along the x-axis and y-axis respectively.

字母 i 和 j 分别表示沿 x 轴和 y 轴的单位向量。

3. Equal and Negative Vectors | 相等向量与负向量

Two vectors are

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