CALCULUS!!!!!
posted by Mathlicious .
Given the vectors a = (1, 3, 4) and b = (4, 5, 4), what is the angle between the two given vectors to the nearest degree?

Calculate the cross product using the matrix determinant rule. That will tell you the sine of the angle.
The magnitudes of the two vectors are
sqrt(1+9+16) = 5.099 and sqrt(16 + 25 + 16) = 7.550
The cross product is
i j k 
1 3 4 
4 5 4 
= 24 i + 20 j 7 k
The magnitude of the cross product is
sqrt (576 + 400 + 49) = 32.015
sin theta = 32.015 /[(5.099)(7.550)]
= 0.8316
theta = 56.3 degrees 
wow, thanks so much :) it really helped.
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