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))`