Vectors: position, geometry and velocity
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 1 worked example, 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- A journey in two numbers
- Writing vectors
- Magnitude and unit vectors
Read the transcript of the teaching part
Last time
Before we start: last time, in The binomial expansion, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
A journey in two numbers
Walk three steps east and four steps north. You end up five steps from where you started, in a particular direction. A vector keeps both facts together: how far and which way. It is the language of motion, force and navigation.
Writing vectors
The unit vector i points one unit east, and j points one unit north. The vector three i plus four j means three east and four north. Column form is the same: three over four. Add and subtract components separately: i with i, j with j. Multiply a vector by a number to scale both.
Magnitude and unit vectors
The magnitude of x i plus y j is the square root of x squared plus y squared. A unit vector has magnitude one. To make one, divide the vector by its magnitude. For three i plus four j, the magnitude is five, so the unit vector is three fifths i plus four fifths j.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Vector geometry · Velocity vectors and moving objects.
The whole chapter: Vectors in Two Dimensions.
Chapter 13: Vectors in two dimensions
- Vectors: position, geometry and velocity 6 min
Also for O Level Additional Maths 4037
Which topics come up most in O Level Additional Maths 4037 past papers, counted from every paper since 2004.