This topic summary covers Knowledge Organiser: Vectors — Basics within Vectors (Basics) for GCSE Mathematics. Revise Vectors (Basics) in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 5 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 7 of 7 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: Vectors — Basics
Key Terms
- Vector: A quantity with both magnitude (size) and direction
- Scalar: A quantity with magnitude only (no direction)
- Column vector: Written as (x, y) — x = right (+) or left (−), y = up (+) or down (−)
- Magnitude: The length/size of a vector, written |a|
- Negative vector: −a has the same length but opposite direction
Must-Know Facts
- Vectors are added by adding components: (a, b) + (c, d) = (a+c, b+d)
- Scalar multiple: k(x, y) = (kx, ky)
- Magnitude: |a| = √(x² + y²) — Pythagoras
- AB = position of B − position of A
- Parallel vectors: one is a scalar multiple of the other
Key Formulas
- Addition: (a, b) + (c, d) = (a+c, b+d)
- Subtraction: (a, b) − (c, d) = (a−c, b−d)
- Scalar multiple: k(x, y) = (kx, ky)
- Magnitude: |a| = √(x² + y²)
Common Mistakes
- Direction of vector: AB = b − a (position of B minus position of A), NOT a − b
- Scalar multiplication: 2a doubles BOTH components — 2(3, −1) = (6, −2)
- Magnitude vs component: |a| = √(x² + y²) is a single positive number — don't confuse with the vector itself
- Adding position vectors: Add component-by-component — do NOT add the magnitudes
Practice questions for Vectors (Basics)
A column vector is written as (3 / −2) (3 on top, −2 on bottom). What does this vector represent?
Explain what it means for two vectors to be parallel. Give an example of a vector that is parallel to a = (2, −3), and one that is parallel but in the opposite direction.
Quick recall flashcards
Vector Addition
Add components separately. (a,b) + (c,d) = (a+c, b+d). Represents combined movement.
Vector Magnitude
|v| = √(x² + y²). Length of vector using Pythagoras. Always positive!