Calculus › Section M · Vector-valued functions › Topic M.4
Tangent and normal vectors
The derivative r′(t) knows two things at once: which way the curve goes and how fast it is being traced. Splitting those apart gives two unit vectors — one along the motion, one in the direction the curve is bending — and they, in turn, split every acceleration into the part that changes speed and the part that changes direction.
In this topic
- Two questions, two vectors
- The unit tangent vector
- Worked example: a tangent line on a helix
- The principal unit normal vector
- Worked example: normals in the plane and in space
- Splitting acceleration into T and N
- Worked example: components of acceleration
- Applied: gravity's split during a kick
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP