. (a) Vectors in R are defined by a = (3,-1, 12) and b = (4,2,3). (i) Determine 4a - 6b. (ii) Calculate a. b. (iii) Find the length of the vector 3a - b. (iv) Determine a x (a x b). (b) Show that the following set of vectors form a basis for R B= 2 -{0) (0) (\)} 5 (c) Determine the change of basis matrix AB such that AE+B[U]E = [u]B, where E ={i, j, k} is the standard basis. Uses your matrix to ex- press the vector [(2,2,1)] E with respect to the basis B from part (b). [2] [2] [3] [4] [5] [9]