WEBVTT
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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.