Question 582471
A)

This is <font color="red">NOT defined</font>. The expression v.w results to be a scalar. Recall that the dot product a.b is only defined if BOTH a and b are vectors (of the same dimension). But since v.w is a scalar, the dot product isn't defined for z.u where z = v.w (because z is a scalar)


B)

This is <font color="red">defined</font>. Both w and u are vectors in R3. So w x u is a vector in R3. If we let z = w x u, then (w x u) x v becomes z x v. So z is a vector in R3. The quantity v is a vector in R3. 


This means that z x v is a vector in R3


Note: keep in mind that the cross product between vectors u and v is only defined if both u and v are vectors in R3 (3-space)