The dot product is a mathematical operation that takes two equal-length sequences of numbers, usually represented as vectors, and returns a single number. It is calculated by multiplying corresponding components of the vectors and then summing those products. For example, if you have two vectors, A = (a1, a2) and B = (b1, b2), the dot product is a1*b1 + a2*b2. The dot product has various applications in physics and engineering, particularly in calculating angles between vectors and determining projections. It is also used in computer graphics and machine learning, where it helps in measuring similarity between data points represented as vectors.