1.       Compute the cosine similarity between the vector pair (1, 2, 3, 4, 0, 1, 0) and (4, 3, 2, 1, 1, 0, 0). Repeat the same computation with the Jaccard coefficient.

2.       Normalize each of the vectors in Exercise 5 to unit norm. Compute the Euclidean distance between the pair of normalized vectors. What is the relationship between this Euclidean distance and the cosine similarity computed in Exercise 5?

3.       Repeat Exercise 5 with the boolean representations of the two documents.

4.       Write a computer program to evaluate the cosine similarity between a pair of vectors.