Recall that example 1.1.7 represented the following sentences by word vectors w = (ncat, ndog, nmat; nat, n. cratched). 1. "the cat and dog sat on the mat" is summarized by the vector a = (1,1,1,1,0). 2. "the dog scratched" is summarized by the vector b = (0,1,0,0,1). 3. "the dog sat on the mat; the cat scratched the dog." is summarized by the vector c= (1,2,1,1,1). (a) (1 credit) find the similarity between pairs of these sentences by calculating the angle between each pair of word vectors. to receive full credit show all your work. (b) (1 credit) what is the most similar pair of sentences? о 1 and 2 0 1 and 3 o 2 and 3