The dot product collapses two vectors into a single number that measures how aligned they are: large and positive when they point the same way, zero when they are perpendicular, negative when they point against each other. That sign is exactly what the collision solver needs later - a negative dot between a relative velocity and a contact normal means two bodies are moving into each other, so an impulse is required; a positive one means they are separating and should be left alone.

Notice Dot(v, v) is the sum of the squares of the components - the squared length of v, which the next lesson turns into an actual length. The perpendicular case returning exactly 0 is the property that makes the dot product a test for “are these at right angles”, and it will matter when you project shapes onto axes for collision detection.