Dot Product

The dot product of two Vectors is a number that tells us how much two vectors point in the same direction.

In simple terms, it is the magnitude of both vectors times the cosine of the angle between the two vectors.

When , the vectors point in the same direction. This is when the dot product is at its largest, because .

When , the vectors are perpendicular to each other.

When , the vectors are opposite each other.

We usually have to compute the dot product a lot. Therefore, a shortcut is to multiply corresponding components and then add.

This formula extends to vectors of any length.