Calculus 3- Very conceptual parametric curve and vector question? Help appreciated!
For the curve f(t)= (t,(t^2),(t^3)), with t E R. Find T(t) and d/dt T(t) for t= -1, 1 and 0.
Find the normals to the planes spaned by these two vectors for the same points in time. What do these planes mean for the movement of the curve? What does the difference between these planes describe?
Re: Calculus 3- Very conceptual parametric curve and vector question? Help appreciate
The plane describes the tangents in both directions and the change in this plane over time tells you how the curve is decreasing geometrically. For example if your plane is sloping downward relative to some direction, then it tells you where the curve is heading (downwards, upwards etc).
Have you calculated the plane equation? (Hint: plane equation is given by n . (r - r0) = 0 where r is any point on the plane and r0 is a specific point).