As far as I understand,
b,X are 3-d vectors, i.e having 3 components. Following representation is of scalar part.
b=[0 1 0]^{T}
X=[x1 x2 x3]^{T}
b x X =
|i j k|
|0 1 0|
|x1 x2 x3|
(I'm not good with latex or any kind of formatting this site uses :( that's just determinant form of Cross Prod.)
You get: x3 along i, 0 along j, x1 along k
i,j,and k are just three unit vectors, representing the dimensions.
So, your resultant vector (scalar part) is : [x3 0 -x1]^{T }
Its like a point in 3-d space (like we did in physics).
Does it help?