The resolution of vectors into components is equivalent to replacing the original vector with the sum of two vectors, whose sum is the same as the original vector. There are an infinite number of pairs of vectors that will satisfy this condition; we choose that pair with one vector parallel to the x axis and the second parallel to the y axis. What difficulties would be introduced by defining components relative to axes that are not perpendicular—for example, the x axis and a y axis oriented at 45° to the x axis?