There are two special types of vectors which have a *magnitude
of 1 *– a vector pointing in the positive x-axis direction, and one pointing
in the positive y-axis direction. The one pointing in the positive x-axis
direction is called ‘i’, the one pointing in the positive y-axis direction is
called ‘j’:

,

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_{}_{}

Unit vectors are often drawn with a little hat above them, like this:

_{}_{}

You can usually assume that ‘i’ or ‘j’ vectors are unit
vectors, whether they have the hat or not. We can use these unit vectors to
describe *any* vector in this coordinate frame. For instance, this
vector:

To describe this vector, we need to look at how many
unit vectors in each direction it goes. For instance, in the horizontal
direction, the vector travels *three* *units* *to the left*,
starting at x = 3 and going to x = 0. In the vertical direction, the vector
travels *two units upwards.* So we can write a description of our vector
by describing how we could make it up with unit vectors:

_{}

Notice how it’s *negative* three _{}. This is
because the unit vector _{} points in the positive x-axis
direction. Because our vector points in the negative direction horizontally, we
need to use *negative* amounts of the _{} vector to describe it.