a = {{a1, a2, a3}, {b1, b2, b3}};
 b = {{e1, e2, e3}, {f1, f2, f3}};
 MatrixForm[Outer[Times, a[[1]], b[[1]]]]
 MatrixForm[TensorProduct[a[[1]], b[[1]]]]
 MatrixForm[Outer[Times, a[[2]], b[[2]]]]
 MatrixForm[TensorProduct[a[[2]], b[[2]]]]

vectorData = Import["/home/vectorData", "Table"];
a = vectorData[[All, {2, 3, 4}]];
b = vectorData[[All, {5, 6, 7}]];