5. Show that c(t) = (t , et, t ) is the flow line of the vector field F(x, y, z) = (-32 , y, -22). 6. a) First sketch the flow line of the vector field T. U(r, y) = y ), (x, y) + (0, 0), 12 + y2' 12+ y2 and b) then solve the flow line equation to find the flow line. 7. a) For a o E C'(R'), define the vector field U(x, y) = (-dy, Pr). Show that div U = 0; b) Given V(r, y) = (y, x), verify that divV = 0 and find a potential function v c C' (R?) such that V = (-vy, (x).9. Use the definition of divergence and curl to verify the formula div(F x G) = G . curlF - F . curlG, where F. G : R* - R are C -vector fields. 10. Calculate V x F, with F(r, y, z) 12 + 12 + 22 (yz, -xz, xy) for (x, y, z) / (0, 0, 0)