Problem 7(Fillin the Blank) : Use the following vector parameterization of a curve to construct a Frenet apparatus in parts 1 through 6.vec(r)(t)=(3t-t3)hat(i)+3t2hat(j)+(3t+t3)hat(k)Problem 7- Part 1(Fillin the Blank) : Find the first, second, and third derivatives of the vector parameterization.For full credit, please apply the rules for derivatives and show the relevant calculations.vec(r)'(t)= vec(r)''(t)= vec(r)'''(t)= Problem 7- Part 2(Fillin the Blank) : Use the alternative formulation to find the unit tangent vector function.For full credit, please simplify algebraic expressions as much as possible and show the relevant calculations. You may use results from part 1.Hint : t4+2t2+1=(t2+1)2hat(T)(t)= Problem 7- Part 3(Fillin the Blank) : Use the alternative formulation to find the unit binormal vector function.For full credit, please simplify algebraic expressions as much as possible and show the relevant calculations. You may use previous results.Hint : t4+2t2+1=(t2+1)2hat(B)(t)= hat(N)(t)=(t)=Problem 7- Part 4(Fillin the Blank) : Use the alternative formulation to find the unit normal vector function.For full credit, please simplify algebraic expressions as much as possible and show the relevant calculations. You may use previous results.hat(N)(t)=(t)=Problem 7- Part 5(Fillin the Blank) : Use the alternative formulation to find the curvature function.For full credit, please simplify algebraic expressions as much as possible and show the relevant calculations. You may use previous results.(t)=Problem 7- Part 6(Fillin the Blank) : Use the alternative formulation to find the torsion function.For full credit, please simplify algebraic expressions as much as possible and show the relevant calculations. You may use previous results.tau(t)=