5. (10 points) Color in computer is often represented as a 3-tuple (r,g,b) where r represents the red component, g represents the green component and b represents the blue component. Each component r,g,b must be an integer between 0 and 255 (inclusive.) For example, a nice lavender color is (199,176,252). White is (255,255,255) and black is (0,0,0). Let A={xN0x255} be the range of each of the rgb components. Let's say that you have 8 different paint colors: Think about how you would describe a measure of "closeness" of two colors. Out of the 8 colors, using your description would you say that A and B should be considered the "closest" pair? What is a function you can use to quantify this idea? Let's consider the cossim formula for two colors v,w : cossim(v,w)=dot(v,v)dot(w,w)dot(v,w) Exercise 1: (4 points) It looks like the two green colors (A and B) should be closest. Compute the dist of these two colors. Exercise 2: (4 points) Consider the two purply colors D and F. Compute the dist of these two colors. Exercise 3: (4 points) Consider the darker green and purply colors B and D. Compute the dist of these two colors. Exercise 3: (for fair effort completeness) (1 point) How do you interpret the results of Exercise 12 and 3? according to the results, would you say the two greens are closer, the two purples are closer or the dark green and dark purple are closer and why? Exercise 4: (for fair effort completeness) (1 point) Is the distance function a good way to compare colors? Why or why not? Can you think of an alternative way that may be better