1. calculate the length of the following paths: f(t) = (7, t, t^2) over 1<t<3 the way i was taught in class to calculate the length of a curve is to integrate the magnitude of the velocity, but i cant seem to naturally integrate the magnitude of (0, 1, 2t) similarly for: f(t) = (cos(3t), sin(3t), 2t^(3/2)) 0<t<4 2. prove the bac-cab formula aX(bXc) = b(a*c) - c(a*b) where * is the dot product what does b(a*c) mean?! how do i evaluate that? i wrote aX(bXc) in terms of the component form, etc. 3. prove the length curve and curvature formulas. 5. prove aX(bXc) = (aXb)Xc + bX(aXc) PLEASE HELP!