Year 10 Foundation · Vectors
Understand what a vector describes
Learn how to read, scale, add and subtract column vectors.
Definition
A vector describes a movement: how far across and how far up or down. It is written as a column, with the across number on top and the up number underneath. A positive top number moves right and a negative one moves left; a positive bottom number moves up and a negative one moves down.
Why Do I Have to Learn This?
Vectors describe movement with both size and direction. They steer ships, planes and characters in video games.
Key Rules:
- 1. The top number is the movement across; the bottom number is the movement up or down.
- 2. To multiply a vector by a number, multiply both parts by it: 3 times the vector (2, 1) is (6, 3).
- 3. To add two vectors, add the tops together and add the bottoms together.
- 4. To subtract, subtract the tops and subtract the bottoms.
- 5. A vector does not have a fixed starting point: the same movement from anywhere is the same vector.
Remember:
- •Across on top, up underneath. Scale both parts; add part by part.
Don’t Forget...
- •Swapping the across and up numbers. A column vector always reads across first, then up, matching coordinates.
- •Multiplying only the top number when scaling a vector. Scaling stretches the whole movement, so both parts multiply.
- •Losing a minus sign when adding. A negative part still adds: 3 + (-2) is 1, not 5.
Translation
Sliding a shape to a new position without turning it.
Moving a shape 3 squares to the right is a translation.
Worked Example:
a is the column vector with 3 across and 1 up. b has -1 across and 4 up. Work out a + 2b.
First find 2b: multiply both parts of b by 2, giving -2 across and 8 up.
Now add a and 2b across the top: 3 + (-2) = 1.
Add the bottoms: 1 + 8 = 9.
Answer: The column vector with 1 across and 9 up
Animated Example:
Free Understand what a vector describes Worksheet
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Let’s Practise the Concept
Step 1 of 3
Put them in order
Tap the numbers from smallest to largest.
In order so far: nothing yet