I have parameterized the intersection of two surfaces. I am given a point and the speed at the point but do not know anything about the velocity other than its magnitude at the point. Is the speed at the point necessary to find the direction? Also known is the direction should be pointing in the decreasing x values. Is the direction just the derivative of the position vector / magnitude of the derivative?
It's not clear to me what you are asking. What does the intersection of two surfaces have to do with the speed of a point? Is the point moving along the intersection? In that case, its velocity vector will be either pointing in the same direction or pointing opposite to the tangent vector of that curve. Use "pointing in the decreasing x values" to decide which, divide the tangent vector by the its own length (magnitude), and multiply by the speed to find the velocity vector.
Originally Posted by MarionButler
Yes a particle is moving according to the intersection of two surfaces. A point and corresponding speed are given at t=0. I need the direction in order to take a directional derivative for the second part of the problem. I was just a little thrown by the speed that is given. Do I really need the speed to calculate the unit tangent I guess is what I really meant to ask.