For the vectors a = (2, −3, 1), b = (0, 5, −1) and c = (−2, 0, 4) find [12 marks] (a) c − a (b) b + c (c) b · c (d) the lengths of a and c (e) the angle between a and c in radians. Question 2. Consider the vectors a = (0, 1, 0), b = (−5, 0, 1) and c = (15, 0, −3). Com- [12 marks] ment on the direction of (a) a and b (b) b − c and c − b 1 (c) b and c (d) Is it possible to express b through c? Give details. Question 3. Consider the basis unit vectors in 3D space: i, j and k. Make a 3D sketch [12 marks] showing the vector v = 2i + 2j + 2k and find the length of v. Question 4. A person prepared a meal of the following items, each having the given [14 marks] number of grams of protein, carbohydrates, and fat, respectively. Beef stew: 25, 21, 22; coleslaw: 3, 10, 10; ice cream: 7, 25, 6. The kilojoule count of each gram of protein, carbohydrate and fat is 17 kJ/g, 16 kJ/g, and 37 kJ/g, respectively. Find the total kilojoule count of each item by matrix multiplication; show your working. Question 5. Given are the matrices [12 marks] A =  3 0 −1  , B =   0 3 1 2 1 −3 −1 2 −4   , C =   0 2 −1   . Find the products AB, BC and AC. Question 6. An irresponsible driver drives the car with acceleration. The distance passed [12 marks] by the car, L, versus time, t, increases according to the formula L(t) = At3 , where A = 50 km/hr3 . Using derivative, find the time moment when the car exceeds the speed limit 100 km/hr