Form a 3-dimensional vector with reasonably random components (for example use your street address, birthdate, etc.). Call this vector u.
We are going to test the randomness of the random vector generator which LINALG uses. The vector u which you created determines a unique plane P through the origin, perpendicular to u. A random vector should be on one side of the plane P or the other. Each side should be equally likely. The test to determine which side a vector lies on is to take its inner product with u, and to see if it is positive or negative.
Create 10 random 3-dimensional vectors, using the random vector generator of LINALG. Name these vectors v1,...,v10. Now compute the inner product of u with each of them. Print the results, and at the top of the page write your name and the numbers of positive and negative inner products.
