solve part B a. Show that n(t) = -g'(t)i + f'(t)j and - n(t) = g'(t)i - f (t)j are both normal to the curve r(t) = f(t)i + g(t)j at thepoint (f(t).g(t)).To obtain N for a particular plane curve, choose the one of n or -n that points toward the concave side of thecurve, and make it into a unit vector. (See the figure to the right.) Apply this method to find N for the followingN-4.P.curves.b. r(t) = 4ti + 4 jPotc. (t) = /16 - 49t i+ 7tj, - stsThe vector dT/ds, normal to the curve, always points in thedirection in which T is turning. The unit normal vectoris thedirection of dT/dsO A. Show that v•T= - 1.O B. Show that n•v= - 1.O C. Show that v•T=0.YD. Show that n•v = 0.Why is the equation from the previous step satisfied?A. The components of n(t) are the components of v(t) with the order swapped and the sign of one changed, so the dot product is 0.O B. The components of n(t) are negative reciprocals of the components of T, so the dot product is - 1.OC. The components of n(t) are negative reciprocals of the components of v(t), so the dot product is - 1.O D. The sum of the components of v(t) is the negative of T, so the dot product is 0.b. N= ( Di+Enter vouur answer in the edit fields and then click Check Answer

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Given - 
r(t) = 4ti + 4e2tjWe know that n(t) = -g'(t)i + f'(t)jwhere f(t) and g(t) functions are…