What is the maximum possible value of the cosine similarity between two vectors?

Let us suppose that you have the following two 4-dimensional word vectors for two words, w1 and w2, respectively:  w1 =(0.2, 0.1, 0.3, 0.4) and w2 = (0.3, 0, 0.2, 0.5) What is the cosine similarity between w1 and w2?Question 6Answera.0.948b.0c. 0.832d.0.5

Cosine similarity is a metric used to measure the similarity between two non-zero vectors in a multi-dimensional space. It's widely used in various fields, including natural language processing, information retrieval, recommendation systems, and more. Cosine similarity is particularly popular in text analysis and document retrieval tasks.

If  and , then the cosine of the angle θ between the two vectors is:

Which code snippet would you use to calculate the cosine similarity between all pairs of books in a dataset, given a TF-IDF matrix tfidf_matrix? similarity_matrix = np.corrcoef(tfidf_matrix)similarity_matrix = tfidf_matrix * tfidf_matrix.Tsimilarity_matrix = np.dot(tfidf_matrix, tfidf_matrix.T)similarity_matrix = cosine_similarity(tfidf_matrix,tfidf_matrix)

Given two documents:Document 1 = 'the best data science course'Document 2 = 'data science is popular'Find the cosine similarity of the two documents.*0.447210.547211.0None of the above