Question

10. Find the work done by the force field F(x,y,z) = z i + x j + y k in moving a particle from the point (3, 0, 0) to the point (0, ?/2, 3) along (a) a straight line (b) the helix x = 3 cos t, y = t, z = 3 sin t 11–12 Show that F is a conservative vector field. Then find a function f such that F = ?f. 11. F(x,y) = (1 + xy)e^{xy} i + (e^y + x^2 e^{xy}) j

          10. Find the work done by the force field

    F(x,y,z) = z i + x j + y k

in moving a particle from the point (3, 0, 0) to the point (0, ?/2, 3) along
(a) a straight line
(b) the helix x = 3 cos t, y = t, z = 3 sin t

11–12 Show that F is a conservative vector field. Then find a function f such that F = ?f.

11. F(x,y) = (1 + xy)e^{xy} i + (e^y + x^2 e^{xy}) j