calc 3 - openstax - derivatives of vector valued functions - tangent vector
- Brian Abbott
Here is a graph exploring the tangent vector that the derivative outputs for the function r(t) = < cos(t), sin(t), t > The vector vr' in the applet below shows that the tangent vector to a curve is similar to our understanding of the derivative in 2-dimensions. In 2-dimensions the derivative represents the slope of the tangent line to our curve at a point. In 3-dimensions, we have that the derivative generates a vector, that when placed at the initial point on the curve to which it is related, is a tangent vector to that curve at the point. To start the animation, click the 'play' icon on the t-value slider (2nd row). Vector u = the derivative vector in standard position (initial point at the origin) Vector vr' = the derivative vector starting at the point on the graph to which it is related Vector vr = the output vector to our vector valued function r(t) = < cos(t), sin(t), t > You may find it helpful to pan the graph view to looking down on the xy-plane (looking straight down the z-axis).