Question

if b1, b2, b3, are vectors, why isnt b1b2b3=0 a subspace?

Answer 1

What do you mean by b1b2b3?

Answer 2

three vectors b1, b2, b3 that when multiplied together yield zero.

Answer 3

So you are talking about the cross-product in ℝ^3 ? Then you still need to quantify how you construct the set which ought to be a subspace.