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Evaluating quantities of vectors

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Two vectors are given by A = -3i + 7j -4k and
B = 6i -10j + 9k. Evaluate the quantities:

a) cos^-1 [A.B/AB] ( the . between the A.B is a dot product)
b) sin^-1 [ |A x B|/AB]
c) Which gives the angle between the vectors.

I haven't a clue as to what to do with this problem. Do I use the cross products of unit vectors to solve this? And if so how do I set up and solve? I would really like to see this worked out completely so I can understand this process. My text book has no example except for listing this formula. I also have the formula C = AB sin theta, is this somehow helpful in solving the above?

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Solution Summary

This solution is provided in approximately 79 words in an attached .doc file. It uses calculations and explanations to determine the quantities of various vectors.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
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