13.1 Vector Functions and Space Curves

Vector Functions

• What is vector functions

  • where a function is made up from component functions

    • IE $r(t)=<f(t),g(t),h(t)>⟹f(t)i+g(t)j+h(t)k$
  • it’s a path in space that is traced in a specific direction as t increases

Space Curves

• What is a Space Curve

  • A closed connection between continuous vector functions

    • suppose that $f,g,h$ are continuous real-valued functions on the interval $I$ then set the C of all points $(x,y,z)$ in space, where
      • $x=f(t),y=g(t)z=h(t)$
      • this equation is called the “parametric equations of C” and t is the parameter
        • We can think of C as being traced out by moving a particle along t and the functions are the path it takes

• Sketching curves

Intersections of vectors