1. True/False:Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample. (a) True or False: For any two vectors u and v in R³, u x v = v x u. (b) True or False: If u and v are two vectors in R3, then u x v=u· v. (c) True or False: If u xv = vxu, then u and v are parallel. (d) True or False: If u, v, and w are vectors in R³, then (u x v) x w = u x (v x w). (e) True or False: The triple scalar product can be used to find the volume of a parallelepiped. (f) True or False: If u, v, and w are vectors in R³, then u · (v x w) = -v · (u x w). (g) True or False: If u and v are nonparallel vectors in R³, u. v = cot 0, where 0 is the angle between then ||ux || u and v. (h) True or False: If u and v are unit vectors in R³, then u x v is also a unit vector.

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