1. Using the examples given above, evaluate the functions and their gradient, divergence and curl operations respectively. . . . GRADIENT o z = x.y z = e(x + y) z = x.e-(x+x) DIVERGENCE A=x.z.a.-ya + 2xy.az A=xa+ya+za A=xy.a-yza+zx.a O O CURL Z O A=ya + (2xy + z).a2yz.a o A=x.y.a,+yz.a,+zx.a o A=x.y.a-yz.a+zx.a. 2. Using the definitions of vector operators in Cartesian system above, prove the following 2 null-identities (analytically) for any vector field "A": Vx(VA)=0 curl of the gradient of any scalar field is zero. V-(VxA)=0 divergence of the curl of any vector field is zero. 3. Prove the 2 null identities using MATLAB. You can select the field functions used in the examples. 4. The characteristic impedance of a medium is defined as the ratio of Electric field and Magnetic Field propagating in that media as shown in the equation below. E, (z) n = Now suppose that you have the data of measured values of Electric Field Ho(z) and Magnetic field in 15 different measurement setups. The resulting values are in the following table: Number of measurements 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Find the average value of impedance. 5. You are given three vectors; Electric Field (V/m) Magnetic Field(A/m) 0.58 0.58 0.53 0.59 0.54 0.61 0.59 0.55 0.51 0.52 0.56 0.55 0.55 0.57 0.55 0.0023 0.0024 0.0021 0.0025 0.0022 0.0023 0.0024 0.0022 0.0020 0.0020 0.0022 0.0021 0.0022 0.0023 0.0022 7 A=i+2j+k. B-= 2i+j+2k C = i +3j+4k Please find the volume of the parallelepiped, formed by three vectors A, B and C by using MATLAB. Write the corresponding code.