Lines on Planes in n-Dimensional Euclidean Spaces

The notation and terminology used here are introduced in the following papers: [1], [5], [12], [4], [9], [14], [13], [8], [15], [6], [2], [3], [7], [11], and [10]. We follow the rules: a, a1, a2, a3, b, b1, b2, b3, r, s, t, u are real numbers, n is a natural number, and x0, x, x1, x2, x3, y0, y, y1, y2, y3 are elements of R . One can prove the following propositions: (1) s t · (u · x) = s·u t · x and 1 t · (u · x) = u t · x. (2) x1 + (x2 + x3) = (x1 + x2) + x3. (3) x− 〈0, . . . , 0 } {{ }