IGCSE Maths / Vectors

Adding and subtracting column vectors

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

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Add and subtract column vectors by working with matching rows: top with top and bottom with bottom. On a grid, addition is one walk followed by another, while subtraction means walking the second vector backwards.

How to add column vectors

Add the top numbers together, then add the bottom numbers together. The rows never mix. On a grid, you can picture this as walking along the first vector, then starting the second walk where the first one ends. Adding is shown as a nose-to-tail walk. The resultant is the single arrow from your starting point to your finishing point. The two routes, a then b or b then a, finish at the same point. This is why a + b = b + a.

How to subtract a column vector

Subtracting a vector is the same as adding its reverse. On a grid, turn the second arrow around, then walk it nose to tail after the first vector. In column working, subtract each row separately. The second vector changes direction when reversed, so each of its components changes sign. Write brackets around a negative number when subtracting it. This makes the double minus clear: taking away a negative adds.

Check signs one row at a time

A negative component means movement in the opposite direction. When a subtraction question has negative components, handle the signs carefully in each row. For example, 4 − (−1) becomes 4 + 1. Use a − b = a + (−b) to remember that subtraction reverses the second vector. The rows never mix, even when both components are negative.

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