Let F be the following vector field: F(x, y, z) =< e-sin(y), e¯"sin(2), e¯* sin(x) >. Find div F Show that there is no vector field G such that curl G = 3yzj + 2ri - xz²k.

Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}

Let F and G be vector fields with differentiable components. Express curl (F x G) in term of div and dot products.

Find the curl of the vector field F(x,y,z)=x^2yi-2y^3zj-3zk.   A. curl F = 2y3i + x2k         B. curl F = -2y3i - x2k         C. curl F = 2y3i - x2k         D. curl F = -2y3i + k