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THThe dot product is a way to combine two vectors to get a single number. You multiply the matching components of the two vectors and then add those results together. For example, if you have two 2D vectors, you multiply the x-values together and the y-values together, then add those two numbers. The result tells you something about how much the two vectors point in the same direction. If the result is zero, the vectors are at a right angle to each other. There’s also a geometric way to understand it: the dot product equals the magnitude of the first vector times the magnitude of the second vector times the cosine of the angle between them—this is written as a · b = |a||b|cos(θ). The dot product is used in many areas, such as physics to calculate work done (when a force is applied along a direction), in computer graphics to find lighting and shading on surfaces, and in machine learning to measure similarity between data points or directions in space.
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