n class we learned about a way to compare two users by taking the Euclidean distance of their 4-tuples. Ne can apply the same logic to compare two titles. Exercise 1: (4 points) For each title, create a 6-tuple where the first entry is the rating of User 1 , the second entry is the rating of User 2 and so on. Exercise 2: (4 points) Which pair of Titles are "closest" and which pair of Titles are "furthest" from each other using the dist metric? (show all 6 calculations.) Exercise 3: (4 points) Which pair of Titles are "closest" and which pair of Titles are "furthest" from each other using the dot metric? (show all 6 calculations.) Ne can use the dot product to define another measure of how similar two titles are. It is called the cosine similarity and for two n-tuples v,w it is defined as: cossim(v,w)=dot(v,v)dot(w,w)dot(v,w) For example, the cossim of (1,1,1,0,1,0),(1,0,0,1,1,1) is: cossim((1,1,1,0,1,0),(1,0,0,1,1,1))=dot((1,1,1,0,1,0),(1,1,1,0,1,0))dot((1,0,0,1,1,1),(1,0,0,1,1,1))dot((1,1,1,0,1,0),(1,0,0,1,1,1))=442=1/2 Exercise 4: (4 points) Compute the cosine similarity of Squid Game with each of the other titles (including itself.) The distance function and the cosine similarity function are two different ways to measure how similar two user ratings are. Exercise 5: (for fair effort completeness:) (1 point) In your own words, what are the differences and similarities of these two functions? Which one do you like better for the task of comparing two titles and why