GCSE(F), GCSE(H),

Vectors can be added and subtracted.

Let `vec(AB) = bb(a) = ((4),(4))`, `vec(BC) = bb(b) = ((5),(0))`, and `vec(AC) = bb(c) = ((9),(4))`

`bb(c) = bb(a) + bb(b) = ((4 + 5),(4 + 0)) = ((9),(4))`

This is the **Triangle Law for Vector Addition**.

The triangle law is **commutative**: it does not matter which way round the vectors are added: `bb(a) + bb(b) = bb(b) + bb(a)`.

Similarly, `bb(c) - bb(b) = bb(a)` (Start at point A, move along the vector **c**, then move in a negative direction along **b** to get to the end point of vector **a**).

The **Parallelogram for Vector Addition** states that the diagonal vector, **g**, is equal to **f** + **e**. The diagonal vector is called the **resultant vector.**

1. Write **a** + **b** as a column vector:

Answer: `((8),(6))`

**a** = `((4),(4))` and **b** = `((4),(2))`

`((4),(4)) + ((4),(2)) = ((8),(6))`

2. **g** = **c** - **d**. Write **g** as a column vector.

Answer: `((7),(7))`

**g** = `((3),(3)) - ((-4),(-4)) = ((7),(7))`

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