Calculus › Section L · Vectors and the geometry of space › Topic L.3
The dot product
Vectors can be multiplied, and the first way, the dot product, turns two vectors into a single number that measures how strongly they point the same way. From that one number come angles, perpendicularity tests, shadows and work.
In this topic
- Multiplying vectors into a number
- The geometric meaning
- Worked example: the angle between vectors
- Perpendicularity
- Worked example: building an orthogonal vector
- Projections: one vector's shadow on another
- Worked example: force and work
- Direction angles and direction cosines
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP