Question: A consumption vector of three goods is defined by x→ = (x1, x2, x3), where x1, x2 and x3 are the quantities consumed of the three goods. A budget constraint is represented by the equation p→·x→ = k, where p→ is the price vector of the three goods and k is a constant. Show that the difference between two consumption vectors corresponding to points satisfying the same budget constraint is perpendicular to the price vector p→.