Science:Math Exam Resources/Courses/MATH152/April 2015/Question B 6 (c)
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Question B 6 (c) 

The matrix represents a rotation in 3D relative to some axis.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

To find the angle of a rotation, once the axis of the rotation is known, select a vector perpendicular to the axis. Then the angle of the rotation is the angle between and 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. From part (b), we know that the direction vector of the axis of the rotation is , then a vector perpendicular to this direction vector is . Now following the hint, we first calculate . The angle between the two vectors is calculated by using the Cosine Formula Thus the angle of rotation is 