| The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages. |
|
Home  Vectors Vector Derivatives Tangent Line and Length of Curves |
|||||
 Search the VIAS Library | Index
|
  |
||||
Tangent Line and Length of Curves
For curves in space we can use the vector derivative to define the tangent line. DEFINITION If X = F(t) is a curve in space and F'(J0) ≠ 0, the tangent line of the curve at t0 is the line with position vector F(t0) and direction vector F'(t0). A vector parallel to F'(t0) is said to be a tangent vector of the curve at t0.
We have seen that the direction of the vector derivative is tangent to the curve. We next discuss the length of the vector derivative. Suppose all the derivatives dx/dt, dy/dt, and dz/dt are continuous on an interval a ≤ t ≤ b. Recall that in two dimensions the length of the curve is defined as the integral
The length of a curve in space is defined in a similar way,
|
|||||
| Home Vectors Vector Derivatives Tangent Line and Length of Curves |
|
||||
Last Update: 2006-11-05