2.

(a) Let E be the electric field given by

E(x, y) = (x - 1)i + (y − 2)j,

where i and j are the unit vectors in the x and y directions respectively.

Find (x, y) (electric potential) that satisfies E = Vo.

(b) Let f be a function of two variables defined by

f(x, y) = ln(x² + y²) + cos(xy)

Let u be the vector defined by

v=i-2j,

where i and j are the unit vectors in the ï and y directions respectively.

Let P be the point of the xy-plane defined by

P =(√TT, VAT)

2

Find the directional derivative of f in the direction of v at the point P.

[5 marks]

[5 marks]