(a) By writing the acceleration in the form of the linear combination of T' and N, prove that J X a d.s Then conclude that the curvature, z, can also be calculated using the form above. (b) Let r(t) = (et cos(t)) i+ (et sin(t)) j + 2 k. Find T(t), the unit tangent vector, N(t), the principal unit normal vector, (c) For the same curve, use the curvature formula we learned in class and the formula from (a) to calculate the curvature. Compare the results to make sure that they match. (d) For the same curve, find the acceleration, a(t), in the form of a linear combination of i, ), and k using the formula d2 a(t) = diz r (t) and in the form of a linear combination of 7' and / using the formula we learned in class. Lastly, compare the acceleration in the two forms to make sure that they match