Here is a graph exploring the tangent vector that the derivative outputs for the function [b]r[/b](t) = < cos(t), sin(t), t >[br][br]The vector v[sub]r'[/sub] in the applet below shows that the tangent vector to a curve is similar to our understanding of the derivative in 2-dimensions. [br][br]In 2-dimensions the derivative represents the slope of the tangent line to our curve at a point.[br][br]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.[br][br]To start the animation, click the 'play' icon on the t-value slider (2[sup]nd [/sup]row).[br][br]Vector u = the derivative vector in standard position (initial point at the origin)[br]Vector v[sub]r'[/sub][sub] [/sub]= the derivative vector starting at the point on the graph to which it is related[br]Vector v[sub]r[/sub] = the output vector to our vector valued function [b]r[/b](t) = < cos(t), sin(t), t >[br][br]You may find it helpful to pan the graph view to looking down on the xy-plane (looking straight down the z-axis).