Consider the following vector function. Please answer the three-part question, the answer choices are listed in the sub-bullets.

r(t)=2t2,sin(t)tcos(t),cos(t)+tsin(t),t>0

Find the unit tangent, unit normal vectors, and curvature T(t), N(t), and k(t).

• T(t)=
  • 1714,sin(t),cos(t)
  • 1712,sin(t),cos(t)
  • 1714,sin(t),cos(t)
  • 1714,sin(t),cos(t)
• N(t)=
  • 0,cos(t),sin(t)
  • 0,cos(t),sin(t)
  • 1714,sin(t),cos(t)
  • 0,cos(t),sin(t)
• Use the formula K(t)=r(t)T(t)to find the curvature
  • 15t1
  • 17t1
  • None