Find a middot a for each of the following n-tuples. (a) a = (2, -1), b = (-1, 1) (b) a = (-1, 3), b = (0, 4) (c) a = (2, -1, 5), b = (-1, 1, 1) (d) a = (-1, -2, 3), b = (-1, 3, -4) (e) a = (pi, 3, -1), b = (2 pi, -3, 7) (f) a = (15, -2, 4), b = (pi, 3, -1) find a middot b for each of the above n-tuples. using only the four properties of the scalar product, verify in detail the identities given in the text for (a + b)^2 and (a - b)^2. which of the following pairs of vectors are perpendicular? (a) (1, - 1, 1) and (2, 1, 5) (b) (1, -1, 1) and (2, 3, 1) (c) (-5, 2, 7) and (3, -1, 2) (d) (pi, 2, 1) and (2, -pi, 0) let a be a vector perpendicular to every vector x. show that a = o.