 Solution

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

Use active rotations on column vectors and positive angles counter-clockwise when viewed from the positive axis toward the origin. Rotation about

z

takes

e_{x}

(cos α, sin α, 0)

e_{y}

(- sin α, cos α, 0)

e_{z}

fixed. These images are the columns of the rotation matrix:

R_{z} (α) = cos α sin α 0 - sin α cos α 0 001 .

It satisfies

R_{z}^{T} R_{z} = I

and

det R_{z} = 1

. Stating the viewing convention avoids confusing this active rotation with a passive change of axes.

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