Question

Let Z ⊂ R^3 be the subspace represented by E_2=0 = 0 and let f on Z be
defined by f{x) = (E_1-E_3)/2. Find a linear extension f ̃ of f to R^3 such
that f ̃ (xo) = k (a given constant), where x_0 = (1, 1, 1)• Is f ̃ unique?