FitProblem 1(30 points)Say that the acceleration function of a particle in space is given by the vector-valued functionvec(a)(t)=(:-sin(t),sec2(t),-cos(t):), with initial velocity vec(v)(0)=(:1,0,0:).Find the curvature of the position function vec(r)(t).Problem 2(25 points)Consider the vector-valued function vec(r)(t)=<53t3+3t+6,4t+3,4t3+4,5t2>.Find the orthogonal decomposition of vec(r)(0) using on the unit tangent and unit normalvectors- vec(T)(t) and vec(N)(t) respectively.Problem 3(20 points)Consider the following scenario...A plane P1is created by the intersection of two lines: l1=(:3,6,2:)+(:-2,1,4:)tand l2=<3,6,2>+<3,-1,-1>s.A vector-valued function is given by vec(r)(t)=Determine if the following two lines intersect. Ifso, give the point of intersection. Otherwise,give the minimum distance between the two lines.L1 : The line which intersects with l1 and l2 that is parallel to the normal vector forP1.L2 : The line tangent to the graph of vec(r)(t)att=0.Problem 4(25 points)Consider the vector-valued function vec(r)(t)=<-4t-12,2t12,2ln(t)>Reparameterize this function in terms of arc length, vec(r)(s).