How to convert vector values to fit k-means algorithm function?
You are 95% there, you just have one hangup...

The vectorization that you are doing is alternatively known as binarization or one-hot encoding.  The only thing you need to do now is break apart all of those vectors and think of them as individual features.  

So instead of thinking of the question one vector as $(0,0,1,0)$ and the question two vector as $(0,1,0,0)$, you can now think of them as individual features.

So this:

-      q1,        q2
-      (a,b,c,d), (a,b,c,d)
user1  (0,0,1,0), (0,1,0,0)
user2  (1,0,0,0), (0,0,0,1)


Becomes this:

-      q1a,q1b,q1c,q1d,q2a,q2b,q2c,q2d
user1  0   0   1   0   0   1   0   0
user2  1   0   0   0   0   0   0   1


And you can think of each one of those binary features as an orthogonal  dimension in your data that lies in a 8-dimensional space. 

Hope this helps!