Posted by Mathlicious on Wednesday, July 2, 2008 at 5:50pm.
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?

CALCULUS!!!!!  drwls, Wednesday, July 2, 2008 at 6:35pm
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

CALCULUS!!!!!  Mathlicious, Wednesday, July 2, 2008 at 6:40pm
wow, thanks so much :) it really helped.
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