Dave's Math Tables: Vectors (Math | OddsEnds | Vectors)

Notation: The lower case letters a-h, l-z denote scalars.Uppercase bold A-Z denote vectors. Lowercase boldi, j, k denote unit vectors. <a, b>denotes a vector with components a and b. <x1, .., xn>denotes vector with n components of which are x1, x2, x3, ..,xn. |R| denotes the magnitude of the vector R.

|<a, b>| = magnitude of vector = (a 2+ b 2)

|<x1, .., xn>| = (x12+ .. + xn2)

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

<x1, .., xn> + <y1, .., yn>= < x1+y1, .., xn+yn>

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

k <x1, .., xn> = <k x1, .., k x2>

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

<x1, .., xn> <y1, ..,yn> = x1 y1 + .. + xn yn>

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

R S= S R

(a R) (bS) = (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 |
R x S = | r1 r2 r3 | = / |r2 r3|   |r3 r1|   |r1 r2| \
| s1 s2 s3 |   \ |s2 s3| , |s3 s1| , |s1 s2| /```

S x R = - R x S

(a R) x S = R x (a S) = a (Rx S)

R x (S + T) = R x S + Rx 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 Rand 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) 