PART C 1 . Redraw the three vectors to clearly illustrate the associative law of addition. (a + b) + c= at(b+c) 2. Define the following terms: a) Zero Vector b) Collinear Vectors THINKING 1. Given: | a | = 20, |b | = 16 and | a + b| = 13. Find | a - b |. Illustrate your reasoning and conclusion with an appropriate diagram. [6] 2. In the parallelogram ABCD, W is the midpoint of BC and the points X and Y are the points of the trisection of AD. Express each of the following vectors in terms of P and q. M B a) BY p b ) MY A X Da c 1. Given the vectors a , b and c b - Sketch vectors: p = a + b + c and q = c - a 2. The magnitudes of 2 vectors are: I c | =3 and Id | =2 . The angle between them is 60 -+ Construct vector P = 2 C - 5d and calculate its magnitude. 3. The diagram shows a square based right pyramid. State a single vector equal to each expression. a) AB + BD - b) AB - AD = d) AE - CD = B) AC + DE + BE E 1) AE - CD + BD - ADGiven vectors: u = (2, -3,-1), v =-31 -4j +k, and w = (-2, 1, 0), find: 4. SHOW YOUR STEPS b) 140-3V+ W/ a) 40 -3v + W 3 bnis d , Bokeventnew 'c) a unit vector in the direction of w. o + d + 6 = q notoby notone PART B 1 . Given the points: E(2, -3, 4), F(5, 1, 2), G(-1, -4, -2), H(-7, -12, 2) Determine whether EF || GH. Explain your result. sabulingam edT 2. The points: A(-1, 2, -1), B(2, -1, 3) and D(-3, 1, -3) are three vertices of parallelogram ABCD. Find the co-ordinates of point C(x, y, z). D 3. A triangle has vertices A(-1, 1, 1), B(2, 0, 3) and C(3, 3, -4). Units are in metres. a) Show that the triangle is right-angled. b) Determine the perimeter of the triangle to one decimal place. c) Calculate the area of the triangle to one decimal place