Vectors

Vectors have both magnitude and direction, as opposed to scalars, which only have magnitude.

Resolving components

You can find the horizontal component / x of a vector when you have its magnitude $d$ and direction $\theta$ using trigonometry:

$$x = d \times \cos(\theta)$$

You can find the vertical component / y of a vector when you have its magnitude $d$ and direction $\theta$ by the same method:

$$y = d \times \sin(\theta)$$

Addition

With a calculator

When adding two perpendicual forces vectors, use the following basic geometric equations: ### Magnitude $F = \sqrt{F_{1}^2 + F_{2}^2} ### Direction$ \theta = \atan(\frac{F_2}{F_1}) $$