The Dot Product

Measuring angles with arithmetic

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $\vec a \cdot \vec b = a_xb_x + a_yb_y = |\vec a||\vec b|\cos\theta$.
• A zero dot product means the vectors are perpendicular.
• Angle between vectors: $\cos\theta = \frac{\vec a\cdot\vec b}{|\vec a||\vec b|}$.

Steps

1. Scaling first
2. The dot product
3. Compute
4. Perpendicular?
5. Find the angle
6. Work as a dot product