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For most of the
problems we will be

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facing in the next few
weeks, we will only

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need to work in two dimensions.

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We use a 2D coordinate system
so we can formally put vectors

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on a grid and more easily
do these vector operations.

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Once we have our axes, the next
thing we need are unit vectors.

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Unit vectors have
a magnitude of 1

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and are in a defined direction.

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For a normal x, y
coordinate system,

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we have i hat in the positive
x direction and j hat

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in the positive y direction.

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In Cartesian coordinates,
the unit vectors

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are the same no matter what
point in space we're at.

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We can also define a unit
vector in the direction

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of an arbitrary vector.

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The key here is to make sure
it has a magnitude of 1.