# Vectors

A vector quantity has both size and direction.

There’s a few way vectors are written. For example if a vector goes 3 units right and 4 units up, is called a and goes from points A to B it could be written as: In an exam though you can just draw an underlined letter like a.

Multiplying Vectors By A Scalar

If you multiply a vector by a positive number it changes its size but not its direction….if the number you multiply it by is negative the direction switches.

Note vectors have arrows on them showing you the direction they go in. Adding and Subtracting Vectors

Exams often ask you to express a movement in terms of two vectors.

a + b means go along a then b.

a – b means you go along a but you go backwards along b. So if you need to find an unknown vector just go along the vectors that are known and decide if they are positive or negative.

Vector Along A Straight Line

You might be asked to prove that vectors that join up are on a straight line…this is done by showing that one vector is a multiple of the other.

So work out one vector…work out the other…then figure out what you multiply one by to get the other (this may be a fraction).

Vectors And Ratios

Ratios can be used with vectors to tell you the lengths of different sections of a straight line. Here’s a good video working you through an exam question on this topic.