Vector Notation

Vector Notation

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 they-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.

Examples

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