Column vectors and magnitude
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 8 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- How far and which way
- Column vectors
- Adding and subtracting
Read the transcript of the teaching part
Last time
Before we start: last time, in Enlargements, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
How far and which way
A pilot is told: fly four kilometres east and five north. That is a vector: a journey with a size and a direction. We write it as a column of two numbers. Adding vectors is joining journeys, and the magnitude is the length of the straight line from start to finish.
Column vectors
A column vector has two numbers. The top says how far across, the bottom says how far up. Positive across is right, negative is left. Positive up is up, negative is down. The vector three, two goes three right, two up. The vector minus one, four goes one left and four up.
Adding and subtracting
Let a be three, two, and b be minus one, four. To add, add the tops and add the bottoms. a plus b is three minus one, and two plus four: two, six. a minus b is three plus one, and two minus four: four, minus two.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Column vectors.
The whole chapter: Vectors.
Chapter 28: Vectors
- Column vectors and magnitude 5 min
- Vector geometry 5 min
Also for O Level Maths 4024
Which topics come up most in O Level Maths 4024 past papers, counted from every paper since 2004.