In: Advanced Math
FOR THE PARAMETRIZED PATH r(t)= e^tcos(πt)i+e^tsin(πt)j+e^tk
a) find the velocity vector, the unit tangent vector and the arc lenght between t=0 and t=1
b) find a point where the path given by r(t) intersects the plane x-y=0 and determine the angle of intersection between the tangent vector to the curve and the normal vector to the plane.