GCSE(F), GCSE(H),

Vectors can be multiplied.

**a** + **a** + **a** = 3**a**

The multiplier of the vector is called a **scalar**. A scalar can take any numeric value, including negative values.

In the example above, **c** = 3**b**. Similarly, **a** = `frac(1)(2)`**d**.

1. State the resultant vector `vec(AB)` in terms of **a** and **b**.

Answer: `4bb(a) + 3bb(b)`

Four instances of **a** along; and three instances of **b** up.

2. What is the magnitude of `2bb(a) + 3bb(b)`, if `bb(a)=((3),(2))` and `bb(b)=((2),(-3))`?

Answer: 13

`2bb(a) + 3bb(b) = 2((3),(2)) + 3((2),(-3)) = ((6),(4)) + ((6),(-9)) = ((12),(-5))`

The magnitude of the vector = `sqrt(12^2 + -5^2)` = 13

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