Vector Crash Course

[TribulationStaff]

Q: What is a vector?
A: A vector is a way of describing motion through space, regardless of the starting point of that motion.

Q: How do you write a vector? In physics, there are two useful ways. The first is polar coordinates. Polar coordinates tells you the magnitude and the direction of the vector. So you could say some vector, say v, is this.

v = r @ theta
For example:
v = 1.75 units @ 30 degrees (or pi/4 radians if you prefer)

However, this is not exactly useful when it comes to the calculations involved. Not, at least, given that most if not all of us are more familiar with Cartesian coordinates. In Cartisian coordinates, the vector tells information about the change in x and the change in y, usually called dx and dy, respectively.

v = <dx,dy>

Based upon the Pythagorean theorem, we can write polar coordinates in terms of Cartesian coordinates and vice-versa.

dx= r*cos(theta)
dy= r*sin(theta)

r^2=dx^2+dy^2
tan (theta)= dy/dx

So, from the earlier example of polar coordinates:

v = <1.299,.75> (roughly)

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