Vectors are defined by both magnitude and direction. Examples of physical vector components are [[Velocity|velocity]], [[Momentum|momentum]] and [[Force|force]]. Vectors are typically defined by bold text or an arrow above the symbol denoting the given vector. Vector components in [[Cartesian Coordinates|Cartesian coordinates]] are defined by a 3 by 1 [[Matrix|matrix]], denoting the $x$, $y$, and $z$ components of the vector. $\vec{a}=\begin{bmatrix}a_x\\a_y\\a_z\end{bmatrix}$ The magnitude of a vector is defined as: $a=|\vec{a}|=\sqrt{a_x^2+a_y^2+a_z^2}$ In two dimensions we will only concern ourselves with the $x$ and $y$ components, understanding that the $z$ component is zero. $a=|\vec{a}|=\sqrt{a_x^2+a_y^2}$ $a_x=a\cos\theta$ $a_y=a\sin\theta$ In two dimensions vector components can also be determined using the angle between the vector and the x-axis, as well as the vector magnitude.