Vectors a, b and c are given as a = (1, -1, 1), b = (-2, 0, 2) and c = (0, 1, 0). (a) Find (a + 2b) · (b - 2c).
(b) Determine which of the vectors a, b and c are perpendicular to each other, if at all. (c) Find the projection of a onto b + 2 c.
(d) Determine the area of the triangle whose vertices are placed in space at a, b and c.
2. Let f(x) = -x 2 + 4x - |x 2 - 1|, -2 ≤ x ≤ 2. (a) Find all of the critical points of f.
(b) Find the maximum and minimum values of f. (c) Sketch the graphs of f and f 0 (by hand) on separate xy-planes. Discuss briefly what is happening at x = -1 and x = 1. (d) Repeat (a) and (b) for the same f, but now with -2 ≤ x ≤ -1.