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Vectors can be represented
through their components.

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If we have a vector
A, we can decompose it

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into its components in
the x and y-directions

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by finding the vectors, one
along x and one along y,

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that add up to
the vector A. This

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is the same thing as finding
the projections of the vector A

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along the x and y-axes.

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Here is the projection
of the vector

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onto the x-axis,
its x-component.

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And here is the projection onto
the y-axis, the y-component.

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This particular vector
could be written

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as A is equal to minus
2i hat plus minus 2j hat.

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A generic vector
in two dimensions

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can be written as A is equal
to Ax, the x-component of A,

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times i hat, the unit
vector along x, plus Ay,

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the y-component, times j
hat, the unit vector along y.

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If the vector is in
three dimensions,

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we will also have
an Az times k hat.

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What if we have the vector
minus 3i hat plus 2j hat?

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First we find the vector
minus 3 times vector i hat

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and add this to the
vector 2 times j hat.

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We can draw this
vector anywhere.

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It doesn't have to
start at the origin.