In Mathematica the dot is used for inner product between two vectors. For your purpose use the asterisk * (or nothing at all, in this case):
a*{1, 1} + b*{3, 4} a{1, 1} + b{3, 4}
In[2]:= Clear[a, b] a {1, 1} + b {3, 4} Out[3]= {a + 3 b, a + 4 b} In[4]:= Times[a, {1, 1}] + Times[b, {3, 4}] Out[4]= {a + 3 b, a + 4 b}
