 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-1/5/c/solution

With the same right-handed active rotation convention as

R_{z}

, the

y

direction is fixed,

e_{z}

rotates towards

e_{x}

, and

e_{x}

towards

- e_{z}

. Therefore

R_{y} (θ) = cos θ 0 - sin θ 010 sin θ 0 cos θ .

Its columns give the images of the three Cartesian unit vectors, which also makes the signs of this rotation matrix explicit.

 New to topics? Read the docs here!