6. Turn in: Given the vector function r(t) =(cos 21 )i + (sin 2t ) j . Find the unit normal vector /V . Simplify your answer when possible 7. Turn in: Find the arc length of the space curve r = (e' cost, e' sint, e' ) over the interval OSIS 2x . As with problem involving sine and cosine, make good use of the trig identities and Algebra to simplify the integral. EXACT anwer required for credit. 8. Turn in: Find the curvature x for the curve r(t) = (cost)i + (sint) j + (t2 ) k at the point ( = 9. Turn in: Find the curvature for the 2-D curve y = xe* at the points x=-2and x=0. You will find that one of them will have a zero curvature. What does it mean when a curve has zero curvature?1. Turn in: An object travels along the path defined by the vector function r = (cos 2t ) i + (sin 3t ) j where t is time in seconds. a) For t between 0, 27, clearly draw the graph of this trajectory. If you do not have a printer, clearly reproduce the graph by hand. b) Determine the positions of the object at t = 5 sec and at t = 6 sec . Then use arrows to clear show the direction of motion from t = 5 sec to t = 6 sec on your graph. 2. Turn in: Use GeoGebra (or a 3-D graphing tool of your choice) to draw the space curve r(t) =(e-)i+(sin 3t) j +(1057) k for Ost$10 If you do not have a printer, clearly reproduce the graph by hand. 3. Turn in: Find the equation for the tangent line to the curve defined by the vector-valued function: r(t) =(sint, 3e', e# ) at the point r(t) =(0,3.1). You can express the equation in parametric or symmetric form. 4. Turn in: Given the vector function "(1) =\\ S V7+1 i+(e")j+- |k with the initial conditions r(0) =(0,0,1) . Determine r(1) = [r'(1) di . 5. Turn in: Given the vector function r(t) =e' (cost)i te' (sint).j + ek . Find the unit tangent vector T at 1=0