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Home Vectors Vector Derivatives Theorem 2:
 
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Theorem 2:

THEOREM 2

Let X = F(t) be a curve in space such that all the derivatives dx/dt, dy/dt, and dz/dt are continuous for a ≤ t ≤ b. Then the vector derivative dX/dt has length ds/dt, where s is the length of the curve from a to t. That is,

|dX/dt| = ds/dt.

PROOF

We have

10_vectors-230.gif

Therefore

10_vectors-231.gif
Home Vectors Vector Derivatives Theorem 2:

Last Update: 2006-11-05