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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