[[Vector|Vectors]] can be added by simply adding the vector components individually: $\vec{a}+\vec{b}=\begin{bmatrix}a_x\\ a_y\\ a_z\end{bmatrix}+\begin{bmatrix}b_x\\ b_y\\ b_z\end{bmatrix}=\begin{bmatrix}a_x+b_x\\ a_y+b_y\\ a_z+b_z\end{bmatrix}$ There are two forms of vector multiplication, dot product and cross product. The dot (or [[Scalar|scalar]]) product can be thought of as the projection of one vector onto another.  The cosine of the angle between both vectors can be used to calculate the dot product: $\vec{a}\cdot\vec{b}=|\vec{a}||\vec{b}|\cos\theta$ $\vec{a}\cdot\vec{b}=a_xb_x+a_yb_y+a_zb_z$ The cross product yields a vector perpendicular to the two input vectors. The direction of the output vector is dependent on the order in which the input vectors are multiplied (reversing the order results in a vector of the same magnitude in the opposite direction). The resultant direction can be determined from the [[Right Hand Rule|right hand rule]]. The magnitude of the cross product is related to the sine of the angle between both input vectors: $|\vec{a}\times\vec{b}|=|\vec{a}||\vec{b}|\sin\theta$ $\vec{a}\times\vec{b}=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\ a_x &a_y &a_z\\ b_x &b_y &b_z\end{vmatrix}=\begin{vmatrix} a_y &a_z \\ b_y &b_z \end{vmatrix}\hat{i}-\begin{vmatrix} a_x &a_z \\ b_x &b_z \end{vmatrix}\hat{j}+\begin{vmatrix} a_x &a_y \\ b_x &b_y \end{vmatrix}\hat{k}$ $\vec{a}\times\vec{b}=\begin{bmatrix}a_yb_z-a_zb_y\\ a_zb_x-a_xb_z\\ a_xb_y-a_yb_x\end{bmatrix}$