Vectors

## Vectors

> NOTE: We will not be using the mathematical notation shown in the video.

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### Vectors and Scalars

- A **scalar** is a quantity. Example: I have 5 apples.
- A **vector** is has a magnitude and direction. Example: 20 mph travelling northeast.

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### Components of Vector

A 2D vector `$$ \vec{a} $$` is made up of an x-component `$$ a_x $$` and a y-component `$$ a_y $$`.

![components of vector](/assets/slides/vectorcomp.png)

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### Magnitude of Vector

From the Pythagorean Theorem.

Where `$$ |\vec{a}| $$` is the "magnitude" of the vector, or its length.

`$$ |\vec{a}| = \sqrt{a_x^2 + a_y^2} $$`

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### Direction of Vector

We may or may not use this. It is likely beyond the scope of this class. But here it is.

`$$ \theta = \tan^{-1}\left(\frac{a_y}{a_x}\right) $$`