# Why are normal unit vectors in a different direction than acceleration vectors?

by Cammy_the_block   Last Updated October 10, 2019 05:20 AM

We learned today in class about normal unit vectors of vector-valued functions. I don't understand why they aren't in the same direction as the acceleration vector.

The acceleration is the second derivative and isn't the normal unit vector just a double scaled version of the second derivative? The magnitude of $$T(t)$$ and $$N(t)$$ act as scalars when they are multiplied to make the vectors unit vectors, right? Therefore wouldn't the direction remain the same as the second derivative? What am I missing?

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