Maxwell's electromagnetic equations in a vacuum are given by; ob (faraday's law) (ampere's law), ▽ . e = 0 (gauss's law), ▽·b-0 (gauss's law for magnetism). 1 oe ▽ x b =-- where e - e(x, y, z, t) and b - b(r, y, z, t), are the electric and magnetic fields, and where c is the speed of light respectively (a) using the equations above, prove (b) prove the following vector calculus identity in r3, where f is a twice continuously differentiable vector field where v72 is the vector laplacian given by (c) hence derive the electromagnetic wave equation 02