Consider the following functions:\

vec(A)=xhat(x)+2yhat(y)-3zhat(z),vec(B)=3yhat(x)-2xhat(y)+zhat(z),f(x,y,z)=xyz.

\ Check the following relations by explicitly calculating each term.\ (a)

vec(grad)*(vec(fA))=f(vec(grad)*vec(A))+vec(A)*vec(grad)f

\ (b)

vec(grad)*(vec(A)\\\\times vec(B))=vec(B)*(vec(grad)\\\\times vec(A))-vec(A)*(vec(grad)\\\\times vec(B))

\ (c)

vec(grad)\\\\times (vec(fA))=f(vec(grad)\\\\times vec(A))-vec(A)\\\\times (vec(grad)f)

2. Consider the following functions: A=xx^+2yy^3zz^B=3yx^2xy^+zz^f(x,y,z)=xyz. Check the following relations by explicitly calculating each term. (a) (fA)=f(A)+Af (b) (AB)=B(A)A(B) (c) (fA)=f(A)A(f)