$$\vec{A}=\vec{A}_xi+\vec{A}_yj+\vec{A}_zk$$ $$A^2=\mathrm{A}_{x}^{2}+\mathrm{A}_{y}^{2}+\mathrm{A}_{z}^{2}$$ $$\vec{A}\cdot \vec{B}=AB\cos\theta$$ $$\vec{A}\cdot \vec{B}=A_xB_x+A_yB_y+A_zB_z$$ $$\left|\vec{A}\times\vec{B}\right|=AB\sin\theta$$ $$\vec{A}\times\vec{B}=\left|\begin{matrix}\hat{i}&\hat{j}&\hat{k}\\A_x&A_y&A_z\\B_x&B_y&B_z\end{matrix}\right|$$

$$\text{Vector Equation:}~~\vec{v}=\vec{r}_0+t\vec{v}$$ $$\text{Parametric Equations:}~~x=x_0+ta,~~y=y_0+tb,~~z=z_0+tc$$ $$\text{Symmetric Equations:}~~\frac{x-x_0}{a}=\frac{y-y_0}{b}=\frac{z-z_0}{c}$$