(a) Consider f(x, y, z) = x + yz, g(x, y, z)= x + xyz +...

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(a) Consider f(x, y, z) = x² + y²z, g(x, y, z)= x + xyz + y³, Compute the gradient and the Laplacian of both f and g. Simplify each result. Show your work. (b) Define ²-0). •-0). B = 1. Which direction does E point? 2. Which direction does B point? 3. Which direction does Ex B point? 4. Compute V. E and V. B. 5. Compute V × E and V × B. Which direction do each of these two vectors point? 6. Compute Vx (Ex B). 1 +y²+z² Simplify the result. Does the result (c) Compute the Laplacian of h(x, y, z) = √x²+y²+z² surprise you? (a) Consider f(x, y, z) = x² + y²z, g(x, y, z)= x + xyz + y³, Compute the gradient and the Laplacian of both f and g. Simplify each result. Show your work. (b) Define ²-0). •-0). B = 1. Which direction does E point? 2. Which direction does B point? 3. Which direction does Ex B point? 4. Compute V. E and V. B. 5. Compute V × E and V × B. Which direction do each of these two vectors point? 6. Compute Vx (Ex B). 1 +y²+z² Simplify the result. Does the result (c) Compute the Laplacian of h(x, y, z) = √x²+y²+z² surprise you?

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a Gradient and Laplacian of f and g The gradient of a scalar function fx y z is given by f fxi fyj f... View the full answer