(1) Let C be a circle of radius 1 centred at the point (x, y) = (0, 1), T the unit tangent vector to C traversed in an anticlockwise direction, and n the unit normal vector to C directed away from the centre of the circle. Consider the vector field F(x, y) = xi+xyj. (a) Calculate f F T ds. (b) Calculate f F n ds. Show all working.

Let (t) (-t + 5, 3e , - 5 sin( – 3t)) Find the unit tangent vector T(t) at the point t =0 T(0) = - Question Help: OVideo Submit Question

Show that the graph of the vector-valued function r(t) =< sin t, 2 cost, √3 sint > is a circle, and find its radius and center.

The position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 6 cos ti + 6 sin tj (3V2, 3V2) (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) = s(t) a(t) (b) Evaluate the velocity vector and acceleration vector of the object at the given point. E) - =