CARTESIAN VECTOR REPRESENTATION

You are dealing in terms of (x,y,z). So what start off with there are the (x,y,z) unit vectors or some may refer to them as normalized vectors. These are:

î, j and k (imagine these have hats over them). These have a magnitude of one and direction is only in their corresponding coordinate axis.

A singular vector will come in the form of

V = aî + bj + ck, where a,b and c are integer coefficients.

The vector can also be denoted as an order pair or triplets depending on its dimensions. For instance:

V = 2î + 3j + 4k this can also be written as…

V = <2,3,4> this is the notation for vectors. Additionally, you see I am holding the vectors such as “V”, you would normally write it on a piece of paper as V(with a hat over it).

Okay now let's go over some definitions.

Magnitude: is a measure of the length of the vector and can give you certain measurements of vectors in context.

To calculate this the following formula is typically used:

Magnitude = sqrt ( (x-coefficient )^2 + (y-coefficient )^2 + (z-coefficient)^2) )

Recognize this? It's the distance formula.

Direction: the direction is a result of the vectors x,y and z components and the unit vectors.

So going over a 2 dimensional vector as an example, W = <2,3>. You use the following formula:

(Y/X) = tan(theta)

Tan^(-1) (Y/X) = theta

Once you find theta and the magnitude you now know the direction and magnitude or length of your vector.

As you can see vectors are a measure of length and direction