For the parametrized plane curve r(t) = < t, t-t,0>: a) Find the velocity vector, the...

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For the parametrized plane curve r(t) =< t, t-t²,0>: a) Find the velocity vector, the speed, the unit tangent vector, the unit normal vector, the acceleration vector and the tangential and normal components of the acceleration vector. Verify explicitly that the unit tangent and unit normal vectors are perpendicular. b) Find the curvature function two ways using both methods discussed in class and show the results are the same. For the parametrized plane curve r(t) =< t, t-t²,0>: a) Find the velocity vector, the speed, the unit tangent vector, the unit normal vector, the acceleration vector and the tangential and normal components of the acceleration vector. Verify explicitly that the unit tangent and unit normal vectors are perpendicular. b) Find the curvature function two ways using both methods discussed in class and show the results are the same.

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