Curve in the space. Consider the curve r(t) = 5 costi +5 sin tj + 2tk....

   

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Curve in the space. Consider the curve r(t) = 5 costi +5 sin tj + 2tk. i) Find the velocity v and the acceleration a of the curve r. ii) Find the unit tangent vector to the curve T. iii) Find the curvature (t) and the radius de curvature p. iv) Find the unit normal vector to the curve N. v) Write the acceleration in the form a = aTTaNN. vi) Find the unit binormal vector to the curve B. vii) Find the arc length of this curve over the interval 0 < t Curve in the space. Consider the curve r(t) = 5 costi +5 sin tj + 2tk. i) Find the velocity v and the acceleration a of the curve r. ii) Find the unit tangent vector to the curve T. iii) Find the curvature (t) and the radius de curvature p. iv) Find the unit normal vector to the curve N. v) Write the acceleration in the form a = aTTaNN. vi) Find the unit binormal vector to the curve B. vii) Find the arc length of this curve over the interval 0 < t