Vectors

Information about

Dot products

Dot products compute the amount that two vectors point in the same direction.

Their most important information is captured by the sign:

• Zero: The vectors are perpindicular.
• Positive: The vectors are generally in the same direction.
• Negative: The vectors are generally in the opposite direction.

Getting more specific than this is useful for projections.

They can be computed:

$$\newcommand\va[1]{ {\color{red} #1_1} } \newcommand\vb[1]{ {\color{blue} #1_2} } \begin{align*} (\va x, \va y) \cdot (\vb x, \vb y) &= \va x \vb x + \va y \vb y \ (\va x, \va y, \va z) \cdot (\vb x, \vb y, \vb z) &= \va x \vb x + \va y \vb y + \va z \vb z \ \end{align*}$$

Projections

Cross Products

Normal Vectors