Math 307: List of Common Formulas

Unit Vector = $\frac{\overrightarrow{v}}{|\overrightarrow{v}|}$

Norm = $|\overrightarrow{v_{i,j,k}}|=\sqrt{(\overrightarrow{v_{i}})^2+(\overrightarrow{v_{j}})^2+(\overrightarrow{v_{k}})^2} $

Express a vector in it’s length and direction is to express the vector as the product of the norm and its unit vector.

$ \overrightarrow{v}=\frac{\overrightarrow{v}}{|\overrightarrow{v}|}*|\overrightarrow{v}| $

Dot Product

With Angle: $Cosθ=\frac{\overrightarrow{u}•\overrightarrow{v}}{|u||v|}$

Without angle: $ \overrightarrow{u_{i,j.k}} • \overrightarrow{v_{i,j,k}} = u_{i}*v_{i}+u_{j}*v_{j}+u_{k}*v_{k} $

Vector Projection formula:

Proj$_{\overrightarrow{v}} ^{\overrightarrow{u}} = \frac{\overrightarrow{u}•\overrightarrow{v}}{|v|^2}\overrightarrow{v}$

Vector projection in vector …