# Vectors

Vectors explained. Reference to questions in c3&c4 book

- Created by: Nicola
- Created on: 24-06-10 01:33

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1

W8.1 Vector algebra

You may or may not have encountered vectors before.

They are quantities which have both magnitude and direction.

Think of them, if you like, as journey vectors,

representing a journey as a straight line, direct from its start to its finish.

We shall also use position vectors

[as the journey from the origin to the given point].

[In M1, we shall use vectors to represent force, acceleration, velocity,

momentum ...]

We shall develop our use of them, first, in two dimensions

and then stretch our results to three dimensions

[a stretch that is done very easily with vectors].

Notation

In geometry, AB can denote a line going from A to B

or the length of that line

[you have to tell from context which it means].

If you intend the line to be seen as a vector,

you must clearly indicate the direction in which the line is to traversed.

On a diagram, this is done by adding an arrow to the line.

You can also modify the name AB by putting an arrow over the letters:

with the name AB.

You can also refer to the vector with a single letter name

which must be in lower case bold: b.

[Upper case bold letters are reserves for the names of matrices

although these are not in our syllabus, we still ought to stick to the convention.]

In handwriting, you can't convincingly do bold,

so any single letter name for a vector must be underlined instead.

Another way of denoting a vector is with a column of numbers.

The vector shown here, which goes along 4 in the x direction and 3 in the y

direction, can be shown as vector .

If point A were the origin, then (4, 3) would be the coordinates of point B.

In you're A-Level work, a row like that will always be intended as a coordinate

pair and a column intended to be a vector.

CT Training 22/02/2010

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