Cross Product & Torque

Areas, perpendiculars and turning forces

An interactive lesson with 8 steps, about 7 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Parallelogram area $= |\mathbf a||\mathbf b|\sin\theta = |a_xb_y - a_yb_x|$.
• The 3D cross product is perpendicular to both vectors (right-hand rule).
• Torque $\boldsymbol\tau = \mathbf r \times \mathbf F$, of size $rF\sin\theta$.

Steps

1. Area from two vectors
2. Set the area
3. From components
4. In three dimensions
5. Unit vectors
6. Torque
7. A spanner
8. The door handle