What Are Vectors? 📏
A **vector** is a mathematical object with both **magnitude** (size) and **direction**. This is different from a **scalar**, which only has magnitude. Vectors are essential for describing quantities like force, velocity, and displacement.
A vector is often represented by an arrow: its length shows the magnitude, and the way it points shows the direction.
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Video: Visualizing Vectors 🎬
Watch this video to understand the difference between a vector and a scalar, and how vectors can be represented.
Practice Problems
Test your understanding of vector components, magnitude, and operations.
1) Find the magnitude of $\vec{v} = \langle 3, -4 \rangle$.
2) Find $\vec{u}+\vec{v}$ for $\vec{u}=\langle 2,5 \rangle$ and $\vec{v}=\langle -1,3 \rangle$.
3) What is $2\vec{u}$ for $\vec{u}=\langle 4,-1 \rangle$?
4) Find the components of the vector from $P(1,2)$ to $Q(5,5)$.
⚡ Vector Speed Quiz
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