# How can we use the cosine similarity formula on document feature vector without a direction?

In mathematics, a vector has both magnitude and direction.

In data science, for identifying document similarity we convert the document into a feature vector. Then apply cosine angle formula between the source and target document's feature vector.

However the cosine formula is applicable only for vectors. And a vector should have both magnitude snd direction. For a document that is represented as a vector, where is the direction?

From this "Cosine similarity measures the degree to which two vectors point in the same direction, regardless of magnitude.

When vectors point in the same direction, cosine similarity is 1; when vectors are perpendicular, cosine similarity is 0; and when vectors point in opposite directions, cosine similarity is -1. In positive space, cosine similarity is the complement to cosine distance: cosine_similarity = 1 - cosine_distance.

For example, the cosine similarity between [1, 2, 3] and [3, 2, 1] is 0.7143."

Also for angle and "Direction", google results says-

Here is a another nice explanation-

https://www.machinelearningplus.com/nlp/cosine-similarity/