The dot product of two vectors is negative when the angle between them is greater than 90 degrees but less than 180 degrees. In mathematical terms, this occurs when the cosine of the angle is negative. The dot product is calculated as:
Dot Product = |A| * |B| * cos(θ)
Where |A| and |B| are the magnitudes of the vectors, and θ is the angle between them. When the angle is between 90° and 180°, the cosine function yields negative values, leading to a negative dot product. This indicates that the vectors point in generally opposite directions to each other.