Dot Product of Two Vectors

If we have two vectors and that are in the same direction, then their dot product is simply the product of their magnitudes: . To see this above, drag the head of to make it parallel to . If the two vectors are not in the same direction, then we can find the component of vector that is parallel to vector , which we can call . and take the product of the magnitudes of and : But how can we find ? If the angle between vectors and is , then we can see that , so . Therefore, in general, we have that the dot product of and is: where is the angle between the two vectors and .