Vectors: Key Exam Points for IB CCEA Mathematics | 向量：IB CCEA 数学考点精讲

📚 Vectors: Key Exam Points for IB CCEA Mathematics | 向量：IB CCEA 数学考点精讲

Vectors are a fundamental topic in IB CCEA Mathematics, appearing in pure mathematics and applied contexts. Mastering vector operations, dot products, and line equations is essential for success in exams. This article provides a comprehensive revision of key concepts, formulas, and common pitfalls.

向量是IB CCEA数学的一个基础主题，出现在纯数学及应用情境中。掌握向量运算、点积和直线方程对于考试成功至关重要。本文对关键概念、公式和常见易错点进行全面复习。

1. Scalar vs. Vector Quantities | 标量与向量

A scalar is a quantity defined solely by its magnitude (size), e.g., mass (5 kg), speed (10 m/s), distance. A vector has both magnitude and direction, e.g., displacement (5 km due east), velocity (10 m/s upwards), force.

标量是仅由大小（数值）定义的量，如质量（5 kg）、速率（10 m/s）、距离。向量有大小和方向，如位移（向东5 km）、速度（向上10 m/s）、力。

In IB CCEA questions, you must identify whether a physical quantity is scalar or vector to apply correct mathematical operations. For instance, adding speeds is straightforward, but adding velocities requires vector addition.

在IB CCEA试题中，你必须识别物理量是标量还是向量，才能采用正确的数学运算。例如，速率相加很简单，但速度相加需要向量加法。

2. Vector Notation and Representation | 向量的记法与表示

Vectors are denoted by bold type in print (e.g., a, v) or by an arrow in handwriting (a⃗). In component form, a 2D vector can be written as a = xi + yj, where i and j are unit vectors along the x- and y-axes. In 3D, a = xi + yj + zk.

向量在印刷体中用粗体表示（如 a, v），手写时常用上方箭头（a⃗）。分量形式中，二维向量可写为 a

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