Vector Voyage

Column vectors 🧭

A **vector** is a movement with a **direction** and a **distance**. We write it as a **column vector** — two numbers stacked: **the top number is the movement ACROSS, the bottom number is the movement UP.** So (3, 2) means 3 right and 2 up; a negative means the other way (left or down).

Read the vector

A column vector has 3 on top and −2 on the bottom. What movement does it describe?

• 3 right and 2 down
• 3 up and 2 right
• 3 left and 2 up
• 3 multiplied by 2

Adding vectors 🔢

To **add** two vectors, add the **top numbers** together and the **bottom numbers** together — the components are kept separate: (2, 1) + (3, 4) = (2 + 3, 1 + 4) = **(5, 5)**. Subtracting works the same way: subtract each component. You never mix the top and bottom numbers.

Add the vectors

An interactive activity.

Order the method

An interactive activity.

Match each calculation to its result

Multiplying by a number ✖️

Multiplying a vector by a plain number (a **scalar**) multiplies **each component**: 2 × (3, 1) = (2 × 3, 2 × 1) = **(6, 2)**. The direction stays the same; the vector just gets that many times longer. A scalar of 3 makes it three times as long.

Scale the vector

An interactive activity.

How long is a vector? 📐

The **magnitude** (length) of a vector is the straight-line distance it moves. Because the across and up parts are at right angles, use **Pythagoras**: **|(3, 4)| = √(3² + 4²) = √25 = 5.** Square each component, add, then square-root — exactly the hypotenuse of a right-angled triangle.

Find the magnitude

An interactive activity.

Plot where you land

An interactive activity.

The voyage rules

In a column vector, the top number is the movement _____ and the bottom number is the movement up. To add two vectors, add their _____ separately. The magnitude of a vector is found using _____.