Edexcel IAL · Mechanics 1
Working with Vectors
Big Idea: A vector is not just a number — it has both a size and a direction, making it the perfect language for describing forces, velocities, and displacements in mechanics.
Chapter Overview
What This Chapter Covers
Vector vs Scalar — why vectors need both magnitude AND direction.
i, j Notation — the standard way to write vectors in Edexcel IAL.
Resultant Vectors — adding forces and other vectors together.
Magnitude — finding the "size" of a vector using Pythagoras.
Direction & Bearings — finding the angle using trigonometry.
Equilibrium — when the resultant force is zero.
Resolving Vectors — breaking one vector into i and j parts.
Newton's 2nd Law — F = ma works with vectors (F and a are vectors; m is scalar).
Topic 1 — What Are Vectors & How Are They Used?
Vectors vs Scalars
Imagine telling someone how to get to a shop. "Walk 500 metres" is not enough — you need to say which direction. That extra information is exactly what makes something a vector.
- A scalar has magnitude (size) only — e.g. mass (5 kg), speed (10 m/s), distance (3 m).
- A vector has magnitude AND direction — e.g. force (7 N east), velocity (10 m/s at 30° above horizontal), displacement (3 m upwards).
Quick test: Could you draw an arrow to represent it? If yes, it's a vector. You can't draw an arrow for "5 kg of mass" — but you absolutely can for "7 N acting to the right."
In Mechanics 1, vectors are used to represent:
- Forces (F) — direction tells you which way the force pushes.
- Acceleration (a) — direction tells you how an object's velocity is changing.
- Velocity (v) — direction tells you where the particle is heading.
- Displacement (s) — direction tells you which way the particle has moved.
Newton's Second Law with vectors: F = ma — here F and a are vectors (they have direction), but m (mass) is a scalar. Multiplying a vector by a scalar just scales its magnitude without changing direction.
Practice Question
Classify each as a vector or scalar: (a) 12 N acting upwards (b) 3 kg (c) 8 m/s heading north-east (d) temperature 25°C
Topic 2 — Vector Notation
i, j Notation & Column Vectors
There are two ways to write a 2D vector in A Level Maths. You need to know both, but always give your final exam answer in i, j notation for Edexcel IAL.
① The i, j Notation
i is the unit vector in the positive horizontal (x) direction — think "right."
j is the unit vector in the positive vertical (y) direction — think "up."
A "unit vector" just means it has a magnitude of exactly 1.
Example: The vector -4i + 3j means: 4 units to the LEFT and 3 units UP.
Example: The vector 3i − 7j means: 3 units to the RIGHT and 7 units DOWN.
↑ j (vertical / up)
|
| * (-4i + 3j)
| · left 4, up 3
|
————+—————————————————→ i (horizontal / right)
|
| * (3i - 7j)
| · right 3, down 7
② Column Vector Notation
Topic 3 — Calculating the Resultant Vector
Adding Vectors Together