Definition

A point is a uniquely identified place in space.

A vector is a directed line segment from point A to point B.

It is directional, and its length can be denoted by |𝑣|

Drawing Vectors

NOTE: When drawing vectors, it is important to notate the direction of the line

Simple draw a line between two labelled points, and mark the direction

Joining Vectors (Geometrically)

Mark out an origin point.

For each item in the vector, draw a line from the previous point to the new location.

After each item has been drawn, draw another line from the tail of the first line (origin) to the head of the last line.
This newly drawn line is the resultant vector

Joining a Negative Vector

Turn that negative vector into something like + (-), where - is the same thing as , but in the opposite direction

Scalar Multiples of Vectors

The lambda symbol () is used to represent the scale of a vector (ie how long it is)

When , the vector travels in the usual direction
When , the vector travels in the opposite direction

When , we get a zero vector, which is just the original point. (???)

A co-ordinate vector (also known as a position vector) is the vector from the origin to a point.

When dealing with vectors in a relative space, we can make use of the origin as an absolute space.

Approaching Geometrical Vector Problems

Take detailed note of the keywords in the question

What type of shape is it, does that shape have special properties that you will need to use?
What is the order of the defined points,

Pay attention to both of these facts.

For example, consider the below parallelogram ABCD

, though

Other vectors exist like , , and their opposites