Question

a=(3;1;-2)
f=(5;1;-4)

E=(-4;3;2)
F=(7;8;-9)
C=(-5;5;4)

Answer 1

cos(α) = a·b/(|a||b|)
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a=(3;1;-2)
f=(5;1;-4)
cos(α) = (3*5+1*1-2*(-4))/(√(3²+1²+2²)√(5²+1²+4²))
cos(α) = (15+1+8))/(√(9+1+4)√(25+1+16))
cos(α) = 24/(√14√42)
cos(α) = 4√3/7
α = arccos(4√3/7) ≈ 8,213°
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E=(-4;3;2)
F=(7;8;-9)
C=(-5;5;4)
EF = F - E = (7;8;-9) - (-4;3;2) = (11;5;-11)
EC = C - E = (-5;5;4) - (-4;3;2) = (-1;2;2)
cos(α) = (11*(-1)+5*2-11*2))/(√(11²+5²+11²)√(1²+2²+2²))
cos(α) = (-11+10-22))/(√(121+25+121)√(1+4+4))
cos(α) = -23/(√267√9) 
cos(α) = -23/(3√267)
α = arccos(-23/(3√267)) ≈ 117,98°