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))`

Start at A and move along vector **a** to point B. Then move to point C using vector **b**. This is equivalent to moving directly from A to C using vector **c**.

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

This is the **Triangle Law for Vector Addition**. This shows that vectors can be added, and from that they can also be subtracted, multiplied and divided.

The **Parallelogram Law for Vector Addition** states that the diagonal vector, **g**, is equal to **f** + **e**. The diagonal vector is called the **resultant vector.** You can get the same resultant vector by adding the vectors in the other order. This shows that adding vectors is **commutative**: it does not matter which way round the vectors are added:

`bb(a) + bb(b) = bb(b) + bb(a)`

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

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

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

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

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

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

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

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