My .md notes for this one maths exam...
INDEX: [Vectors] [Matrices] [Functions] [Graph Theory]
Notes:
-a- -b- -c- ("a bar, b bar, c bar") is how i write vector notation
^i^ ^j^ ^k^ ("i hat, j hat, k hat") is how i write unit vector notation: unit vectors define what the size of basic unit / measurement of a vector is (typically 1)
a:i a:j a:k means the i, j and k properties of vector a
Formulae:
|-a-| (magnitude of -a-): sqrt((a:i)^2 + (a:j)^2)
-a- --> ^a^ (get unit vector of vector): -a- / |-a-|
-a-.-b- (dot product of two vectors): (a:i * b:i) + (a:j * b:j)
cos(θ) (get cosine of theta: smallest angle between -a- and -b- in radians): (-a-.-b-) / (|-a-| * |-b-|)
θ (get theta: smallest angle between -a- and -b- in radians): arcCos((-a-.-b-) / (|-a-| * |-b-|))
-a- x -b- (cross, not multiply: cross gives you the tendency of both vector's directions (if you are using 2D vectors, sub ^k^ in with 0)):
| ^i^ | ^j^ | ^k^ |
|---|---|---|
| a:i | a:j | a:k |
| b:i | b:j | b:k |
result vector ^i^ = (a:j * b:k) - (a:k * b:j)
result vector ^j^ = - ((a:i * b:j) - (a:j * b:i))
result vector ^k^ = (a:i * b:j) - (a:j * b:i)
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