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\displaystyle 2\mathbf{b}\, –\, \mathbf{c} + 3\mathbf{d} = 2(3, -1) – (-2, 4) + 3(1, 2) = (11, 0);

\displaystyle \displaystyle \mathbf{e} = \frac{(11,0)}{\sqrt{11^2+0^2}} = (1,0) = \mathbf{e_x}