IGCSE Maths / Vectors

Column vector notation

Edexcel International GCSE Maths (4MA1), chapter 27: Vectors, specification point 5.1b. Free lesson.

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A column vector records a move: the top number gives the across movement and the bottom gives the up movement. You need to write it in the right layout and distinguish it from a coordinate, which gives a place.

How to read a column vector

A column vector is two numbers stacked in a bracket. Its layout tells you what the numbers mean: the top is the move across and the bottom is the move up. Right and up are positive, so negative numbers mean left or down. In (x, y), the numbers are side by side with a comma. In a column vector, they are stacked with no comma. For example, (3, −2) is a coordinate, but the column vector with top number 3 and bottom number −2 is a move 3 right and 2 down.

A coordinate is a place, but a vector is a move

A coordinate tells you where a point is on the grid. A column vector tells you how far to travel across and up, but not where you start or finish. The same vector describes the same move from any starting point. In a coordinate, the first number shows how far right of the origin the point is. In a vector, it shows how far right you travel. A negative coordinate places a point left of the origin or below it. A negative vector number means the move goes left or down.

Find the vector between two points

To find the vector from a starting point to a finishing point, subtract the start coordinates from the finish coordinates. Do this in both rows, with the across movement on top and the up movement underneath.

Reverse a vector

Reversing a journey changes the direction of both movements. So the vector from B to A has the opposite signs to the vector from A to B. If →AB = [5; −2] as a column vector, then →BA = [−5; 2] as a column vector. Reversing a vector flips both signs.

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