# What are the formulas to sum two 2D vectors?

I'm writing a PHP algorithm to calculate the sum of two 2D vectors with the same origin, given their intensity and their angle with a given axis. How to calculate the properties of the sum vector? I have some ideas about the intensity (Pythagorean theorem and Carthesian components), but I don't have a clue of how to calculate the angle.

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What you need is to convert the polar notation to cartesian, add the components and covert back to polar. – ja72 Dec 18 '12 at 15:25

If your resultant vector is $c$ and $\hat c = c/|c|$, then $\hat c \cdot \hat x = \cos \theta$ and $\hat c \cdot \hat y = \sin \theta$, where $\hat x, \hat y$ are the unit vectors in the x- and y-directions and $\theta$ is the angle $c$ makes with respect to the x-axis.

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What is $\hat c = c/|c|$? – Giulio Muscarello Dec 18 '12 at 17:57
$\hat c$ means the unit vector in the direction of $c$. $c/|c|$ is a way of calculating this unit vector. – Muphrid Dec 18 '12 at 18:11