I need to determine the matrix that represents the following rotation of

.

(a) angle

, the axis

(b) angle

, axis contains the vector

(c) angle

, axis contains the vector

Now, I would like to check if I got the right answers because this problem has been quite difficult for me. Any help is greatly appreciated.

Please forgive me for skipping the work because formatting matrices is a real pain. Especially when I have a lot of them.

For part

, I got that

is an orthonormal basis of

. Then after simplification, the matrix is

For part

, I got an orthonormal basis as

.

Then after simplification, the matrix is

Is what I have done so far correct such that I can proceed with part

?