a) Let u :(2,1,3), v = (-1, 4, 2) and w :(0,], 5) are vectors in R3. i. Express the vector (2, 2, 8) as a linear combination of u, v and w. ii. Find the volume of the parallelepiped determined by the vectors u, v and w. b) The plane H passes through the points P (-1, 3, -2), Q(4, -l, -l) and R(3, 0, e), where c is a constant. i. Find, in terms of 5, x iiiQ Given that x E = 3i + dj + k , where d is a constant, ii. find the value of e and show that d = 4, 3 3 4 (c) Given that A = 2 0 2 4 2 k i. Show that det A = 20 4k. ii. Find A']