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Mathematics LibreTexts

1.7: Space Curves

  • Page ID
    192866
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    Learning Objectives
    • Write the general equation of a vector-valued function in component form and unit-vector form.
    • Recognize parametric equations for a space curve.
    • Describe the shape of a helix and write its equation.
    • Define the limit of a vector-valued function.
    • Write an expression for the derivative of a vector-valued function.
    • Find the tangent vector at a point for a given position vector.
    • Find the unit tangent vector at a point for a given position vector and explain its significance.
    • Calculate the definite integral of a vector-valued function.

    Our study of vector-valued functions combines ideas from our earlier examination of single-variable calculus with our description of vectors in three dimensions from the preceding chapter. In this section, we extend concepts from earlier chapters and also examine new ideas concerning curves in three-dimensional space. These definitions and theorems support the presentation of material in the rest of this chapter and also in the remaining chapters of the text.

     


    This page titled 1.7: Space Curves is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Kenn Huber.