math - Finding the angle between two lines -

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possible duplicate:
calculating angle between 2 lines without having calculate slope? (java)

i need find angle between 3 points. have point , point c being 2 points of ray , have point b being central point points , c extend from. if create line between points b , a, , create line between points b , c, can find angle between 2 lines.

take line direction vector a(a,a',a") , line b direction vector b(b,b',b").

        a.b = ||a||.||b||.cos(t)                       a.b         cos(t) = --------------                   ||a||.||b||

take a(1,2,3) ; b(4,5,6) ; c(3,2,0) calculate angle between lines ab , ac. line ab has direction numbers (3,3,3) , line ac has direction numbers (2,0,-3). hence

                6 + 0 - 9     cos(t) = -----------------              sqrt(27) .sqrt(13)

update:

use arccos(cos(t)) obtain angle. convert radians degrees multiply 180/π convert degrees radians multiply π/180


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