Concept 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.

Core Idea

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.

Understanding

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.

Question

Worked Example

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

Select an answer to see the explanation