Dot product
Definition
$$\vec u=(u_1,u_2,u_3),\qquad \vec v=(v_1,v_2,v_3).$$
Formula
$$\boxed{\vec u\cdot\vec v=u_1v_1+u_2v_2+u_3v_3}$$
Example
$$\vec u\cdot\vec v=(2)(1)+(-1)(4)+(3)(-2)=2-4-6=-8.$$
Geometric interpretation
$$\boxed{\vec u\cdot\vec v=\|\vec u\|\,\|\vec v\|\cos\theta}$$
$$\cos\theta=\frac{\vec u\cdot\vec v}{\|\vec u\|\,\|\vec v\|}.$$
Important properties
Practice activity
Practice: Dot product
Instructions:
📌 Random exercise
Step 0 of 5