3. Prove the following vector identities: a. V(uv)= uVv + vVu b. V.(uA)= u(V.) + (Vu)....

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3. Prove the following vector identities: a. V(uv)= uVv + vVu b. V.(uA)= u(V.Ā) + (Vu). Ā c. V.(ĀxB)= B.(VxĀ) - A.(VXB) d. V(UA)= u(VxĀ) - AX(Vu) where u(x,y,z), v(x.y.z) is a scalar field; A (x.y,z), B (x.y,z) is a vector field. 3. Prove the following vector identities: a. V(uv)= uVv + vVu b. V.(uA)= u(V.Ā) + (Vu). Ā c. V.(ĀxB)= B.(VxĀ) - A.(VXB) d. V(UA)= u(VxĀ) - AX(Vu) where u(x,y,z), v(x.y.z) is a scalar field; A (x.y,z), B (x.y,z) is a vector field.