Exercises 27–32 concern several identities for vectors a , b , c , and d in R 3 . Each of them can be verified by hand by writing the vectors in terms of their components and by using formula (2) for the cross product and Definition 3.1 for the dot product. However, this is quite tedious to do. Instead, use a computer algebra system to define the vectors a , b , c , and d in general and to verify the identities.
(a×b)×(c×d) = [a · (c×d)]b − [b · (c×d)]a.
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