Something like this?

Transpose[{1, 2, 3} RandomReal[{-1, 1}, {3, 10}]]

(* Out[373]= {{0.981734293226, 
  0.684303054, -0.437793709387}, {-0.0362668999938, -1.20283477061, \
-1.33978431487}, {0.375630986245, 
  0.592477784197, -1.13340532819}, {-0.722525173953, -0.659695292216, \
-2.70412310576}, {0.138754748527, 0.042501729885, 
  0.280926778119}, {0.970810465664, 
  1.22555900094, -1.23595811685}, {0.246593090112, -0.982459686448, 
  2.91243740985}, {-0.800383383347, 1.24284223826, 
  1.69913760441}, {0.442353700026, 0.932816130511, 
  1.63156023223}, {-0.82593776151, 0.0130059873043, 0.307173349828}} *)