Let F be the vector field (sin x,ey²) and C be the ellipse x? + 5y² = 1, oriented counterclockwise. Calculate F. dr

Assume that an object is moving along a parametric curve and the three vector function. T (t), N(t), and B (t) all exist at a particular point on that curve. CIRCLE the ONE statement below that MUST BE TRUE: (a) B. T=1 (b) T x B = N (B is the binormal vector.) v (t) (c) N (t) = |v (t)| (d) N (t) always points in the direction of velocity v (t). (e) a (t) lies in the same plane as T (t) and N (t).

Find a vector function that represents the curve of intersection of the paraboloid z = 5x² + 2y² and the cylinder y = 3x². Use the variable t for the parameter. r(t) = (t,