Please help, this is for calculus 3. Vector valued functions and space, motion in space.

David S. Loyola Metallurgical & Materials Engineering Center for Non-Ferrous Structural Alloys MS Stringer 5. Consider the vector-valued function given below r'(t) = 2ti + 2 cos(t) / + 2 sin(t) k (a) This curve has a special name. What is that name? (b) Make a graph of this curve using technology for -2:t S t - 2nt. Attach a screenshot/printout of your graph to this assignment. Do not submit a link to an online file. (c) Find the unit tangent vector when t = 0 (d) Find the unit normal vector when t = 0 (e) Find the binormal vector when t = 0 6. Sketch a graph of r(t) = (cos3 t, sin' t) for 0 S t S 2nt. This curve is called a hypocycloid. Attach a screenshot/printout of your graph to this assignment. Do not submit links to online files.) Find the length of this curve.gineerin tural Al 7. Consider a circle defined with the vector-valued function ?' = (R cost , R sint) where R > 0. Show that all circles defined as such have constant curvature. What is that curvature? 8. Recall the scalar product rule from page 59 of the Guided Notes Template - If (t) u(t) ] = f'(t) u(t) + f(t)u'(t) and suppose u(t) = (Ux(t), Uy(t), Uz(t)). Use this information to prove the scalar product rule