Bla. A scalar field is described by the equation f(x,y) = xe. Use a sketch to illustrate what the field looks like. [5] b. Write down the vector that represents the gradient at an arbitrary point u,v. Evaluate the vector that describes the direction of the field gradient at x=0, y=2. Comment on your answer. [6] c. Consider a vector field given by xi+yj. Sketch the field. What word might be used to describe it? [5] d. Use the concept of a unit vector to obtain an expression for a displacement field in which the magnitude is given by f(x,y) = xe and the direction is given by xi+yj [6] e. If the displacement vector field is written in the form u = ux(x,y)i + uy(x,y)j what are the expressions for ux, uy, in the example displacement field above? [4] f. Obtain an expression for the strain tensor, consistent with the description of the displacement field u described in (e) above. [2] The above example explores strain in 2D. How many components does the generalised 3D stress tensor contain? Within the stress tensor matrix, where are the tension/compression components to be found? [2]