Which SQL statement correctly adds a VECTOR column named v with 4 dimensions and FLOAT 32 format to an existing table named my_table?

The statement that accurately adds a VECTOR column named v with 4 dimensions and FLOAT 32 format to the existing table my_table is constructed correctly in terms of syntax and intent. When you need to introduce a new column to a database table, the SQL command typically utilized is ALTER TABLE followed by the ADD clause.

In this case, the correct form specifies the new column's name, the type of data it will hold (in this case, VECTOR), and the specifications regarding the dimensions and data format (4 dimensions and FLOAT32). This clarity in defining the properties of the new column aligns with standard SQL syntax conventions.

The addition of the VECTOR type indicates that the database can handle multi-dimensional array-like data specifically designed for vector search applications, which is essential in contexts such as machine learning and AI.

The other options do not adhere to the correct SQL syntax for adding a column. Specifically, modifying an existing column with a VECTOR type is not achievable through a MODIFY statement, and an UPDATE statement is not applicable since it is used for changing data in existing records rather than adding new columns.