GCSE(F), GCSE(H),

**Vectors** are quantities that have both a magnitude and a direction.

Write the vector in a column, with the movement in the *x*-direction being the top number and the movement in the*y*-direction being the bottom number.

A vector `((5),(7))` gives a displacement in the positive *x* direction, and 7 in the *y* direction.

Vectors are written in a number of ways.

The vector may be written to indicate the start and end points: `vec(AB)`. Direction is important: the vector is a displacement from A to B.

The vector can also be shown as a single letter: this is printed as **a** (bold a). When writing by hand, underline the letter: `ul(a)`.

Note that `vec(AB) = ul(a) = `**a**.

A column vector gives both magnitude and direction. The magnitude, or size, of a vector is written as |a| (called **modular** a). This means that the direction (when considering the size) is irrelevent and can be obtained using Pythagoras: for a vector `((x),(y))`, this is `sqrt(x^2 + y^2)`.

A vector that is equal to another vector has the same magnitude and direction, although they may not necessarily be at the same location.

Vector `vec(AB) = -vec(BA)`.

If vector `vec(AB)` = **a** and `vec(BA)` = **b**, then **a** = - **b**.

1. Vector **a** is defined as `((-3),(-4))`. Vector **b** is defined as `((4),(3))`. Does **a** = -**b**?

Answer: No; neither the *x*-displacement nor the *y*-displacement are equal and opposite.

2. Vector **c** is defined as `((7),(11))`. What is the magnitude of **c**?

Answer: 13.04 (to 2dp)

Use Pythagoras to determine the magnitude:

magnitude = `sqrt(7^2 + 11^2)`

= 13.038

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