Question 4 (10 points) a) Determine the value of k such that the vectors (1, 2, 1) and (k, 2k + 1, 8) are perpendicular. [3 marks, Exp C1] b ) i) Use the cosine law to show that atb = a + b|2 - 2d . b (Hint, it might be helpful to draw a diagram) ii) Use the proof from part i) to solve the following: If m and n are both unit vectors and if m + n = V3, find the value of (2m - 5n) . (2n + 5m)