Dave's Math Tables: Vectors |

(Math | OddsEnds | Vectors) |

** Notation:** The lower case letters a-h, l-z denote scalars.Uppercase bold

|**<**a, b**>**| = magnitude of vector = (a^{ 2}+ b^{ 2})

|<x_{1}, .., x_{n}>| = (x_{1}^{2}+ .. + x_{n}^{2})

**<**a, b**>** + **<**c, d**>** = **<**a+c, b+d**>**

**<**x_{1}, .., x_{n}**>** + **<**y_{1}, .., y_{n}**>**= **<** x_{1}+y_{1}, .., x_{n}+y_{n}**>**

k **<**a, b**>** = **<**ka, kb**>**

k **<**x_{1}, .., x_{n}**>** = **<**k x_{1}, .., k x_{2}**>**

**<**a, b**>** **<**c, d**>** = ac + bd

**<**x_{1}, .., x_{n}**>** **<**y_{1}, ..,y_{n}**>** = x_{1} y_{1} + .. + x_{n} y_{n}**>**

**R** **S**= |**R**| |**S**| cos ( = angle betweenthem)

**R** **S**= **S** **R**

(a **R**) (b**S**) = (ab) **R** **S**

**R (S** + **T**)= **R** **S**+ **R** **T**

**R R** = |**R**|^{ 2}

**|R** x **S|** = |**R**| |**S**| sin ( = angle betweenboth vectors). Direction of **R** x **S** is perpendicularto **A** & **B** and according to the right hand rule.

| i j k |RxS= | r_{1}r_{2}r_{3}| =/|r_{2}r_{3}| |r_{3}r_{1}| |r_{1}r_{2}|\| s_{1}s_{2}s_{3}|\|s_{2}s_{3}| , |s_{3}s_{1}| , |s_{1}s_{2}|/

**S** x **R** = - **R** x **S**

(a **R**) x **S** = **R** x (a **S**) = a (**R**x **S**)

**R** x (**S** + **T**) = **R** x **S** + **R**x **T**

**R** x **R** = 0

If a, b, c = angles between the unit vectors **i**, **j**,**k** and R Then the direction cosines are set by:

cos a = (**R** **i**) / |**R**|; cos b = (**R** **j**) / |**R**|; cos c = (**R** **k**) / |**R**|

|**R** x **S**| = Area of parrallagram with sides **R**and **S**.

Component of **R** in the direction of **S** = |**R**|cos = (**R** **S**) / |**S**|(scalar result)

Projection of **R** in the direction of **S** = |**R**|cos = (**R** **S**) **S**/ |**S**|^{ 2} (vector result)