 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2013-resit/10/a/ii/solution

With the same active rotation convention, the

x

axis remains fixed, while

e_{y}

moves toward

e_{z}

. Therefore

R_{x} (β) = 100 0 cos β sin β 0 - sin β cos β .

For instance, a positive quarter-turn maps

e_{y}

e_{z}

and

e_{z}

- e_{y}

, checking both signs. This is again an orthogonal matrix of determinant one.

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