Column vectors

We know a vector can be represented by a line which has magnitude (how long it is) and direction.

In graphical vectors, this is represented by:

Column vectors are measured with an X and Y axis

or as a column vector $((3),(4))$

That is

Take a vector and measure its y axis and then its x axis then white them above one another

Put the X above the Y axis measurements coordinates are measured alphabetically first

NOTE:

(Do not get confused between coordinates (3,4) which is the position of a point $x$ along and $y$ up from zero).

In column vectors, the numbers represent a distance and direction from any point.

In column vectors $x$ is on the top and $y$ is on the bottom. For coordinates we have:

Coordinates are written alphabetically
so X comes before Y (X,Y).

But in column vectors so does $x$ come before $y$ .

Remember X becomes before Y in the alphabet so the X axis above Y on the bottom

Example 1

Convert the vector $vec (AB)$ to a column vector.

Measure this example vector and draw the resulting axis in order

Vector $vec (AB)=((3),(2))$