知识点 8

Interpret and perform simple vector operations (components, magnitude, addition, scaling) when presented.

Add, subtract, and scale vectors by components, and use magnitude only when asked.

核心知识

Treat a vector as directional movement by components. Add and subtract vectors component by component, and use $\sqrt 𝑥 2 + 𝑦 2$ only when the question asks for magnitude.

深入理解

Rule: ACT vector questions are usually procedural.

If a vector is written in components, each coordinate tells you how far and in what direction the movement goes. Addition, subtraction, and scaling happen entry by entry. The common mistake is to mix vector operations with distance formulas when the problem only asks for the resulting components.

题目

示例解析

In the coordinate plane, $𝐯 = ⟨ 3, - 2 ⟩$ and $𝐰 = ⟨ - 1, 5 ⟩$ . What is $𝐯 + 𝐰$ ?

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