Calculate divergence and curl

Question

Consider the vector field

a = (-78.y^2.z+17.x^2)i + (11.x^2.z-21.y.z^2)j + (93.x.y^2-33.x.y)k

a) calculate the divergence of a

b) calculate the curl of a

Answer 1

F = Pi + Qj +Rk = (-78y²z+18x²)i + (11x²z-21yz²)j + (93xy^2-33xy)k

a)

div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z

= 36x +21z² + 0 = 36x +21z²

b)

curl F = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

= (186xy-33x +78y²)i + (11x²-42yz -93y²+33y)k + (22xz +21z²)k