Solve 11.1 by integrating F.dr from points A to B as found in problem 11.2. Mathematical Methods for Physics and Engineering: A Comprehensive Guide 11.10 Exercises 11.1 The vector field F is defined by F = 2xzi + 2yzj + (x + 2yz ? 1)k. - Calculate Vx F and deduce that F can be written F= Vo. Determine the form of . Q = [3x(y +z) + y

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Solve 11.1 by integrating F.dr from points A to B as found in problem 11.2.
Mathematical Methods for Physics and Engineering: A Comprehensive Guide
11.10 Exercises
11.1 The vector field F is defined by

Mathematical Methods for Physics and Engineering: A Comprehensive Guide 11.10 Exercises 11.1 The vector field F is defined by F = 2xzi + 2yz²j + (x² + 2y²z ? 1)k. - Calculate Vx F and deduce that F can be written F= Vo. Determine the form of . Q = [3x²(y +z) + y³ + z³] i + [3y²(z + x) + z³ + x³] j + [3z²(x + y) + x³ + y³] k. Show that Q is a conservative field, con- struct its potential function and hence evaluate the integral J = f Q. dr along any line connecting the point A at (1, ?1, 1) to B at (2, 1, 2). 11.2 The vector field Q is defined by

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