Multiply length by length by the cosine of the angle to get a single number, a·b=|a||b|cosθ, which measures how much the two are in sync.
Module goal. Introduce the operation that multiplies two vectors into a number, capturing the angle between them, projection, and when they're perpendicular.
eastmath.com · 27.4 The Dot Product: Angles and Perpendicularity · 27.4.2 Defining the Dot Product