Calculus › Section L · Vectors and the geometry of space › Topic L.4
The cross product
The dot product turns two vectors into a number; the cross product turns them into a third vector, one standing perpendicular to both. That single construction unlocks areas, torque and volumes.
In this topic
- A vector perpendicular to two vectors
- The determinant shortcut
- Worked example: computing a cross product
- Direction and order
- Length as area
- Worked example: area of a triangle in space
- Torque: the cross product in action
- The triple scalar product
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP