Up vector and angle to rotation matrix

Hi,

I got this problem that i'm trying to turn a vector and angle into a 3x3 rotational matrix, but in a special way that it's guaranteed the vector i use will be the up vector (or second column.. or row im not sure) of the resulting matrix.

(So far i found solutions on how to turn a vector and angle into a matrix but the results don't suit my needs, e.g. turning the vector [0,0,1] and any angle results in a rotation matrix where the forward vector (or heading?) is [0,0,1], vector [0,1,0] and any angle results that the up vector is [0,1,0] etc.)