Question

3-D rotation matrix

choose a couple of specific angles like pi/6 , pi/4 ...and write the arithmetic values and rotate a vector of your choice as an example application.

Answer 1

First you understand the construction of rotation matrix in two dimension. I am attaching the construction

now for 3D,the rotational matrix will take form

note that alpha is an arbitrary angle so you may choose it pi/6 or pi/3, whatever you want. Note that n dimensional rotational matrix in Mn(R) are orthogonal matrix.

I am extending the answer here. Final Answer