1. State whether each quantity is a vector or scalar. Explain. (5 marks) a. Speed b. Velocity c. Weight cl. Mass e. Area 2. In the diagram, ACE is an equilateral triangle. B, D, and F are the midpoints of AC, CE, and EA. AB = f and AF 2 f. (6 marks) Write the following in terms of E' and T'. 4 a. AC Q b. AD _\\ c. CE 4 d. EB A Give an example of a vector that is equal to: e.2v _\\ A f.u'u 3. Draw diagrams to show two vectors and i and the vectors i l b and ' b . (6 marks) a. When is the magnitude of H' + i more than that of i ?7 b. When is the magnitude of i + ? less than that of H' T"? c. When is the magnitude of i + ? equal to that of a ?? cl. When is l 3" = ll + l?'? e. When is the minimum value of 'E' +5 I? 4. A boat sails 3 km South, then 10 km Southeast. Use trigonometry to find the boat's distance and bearing from its starting point. (6 marks) 5. Convert the following vectors; (4 marks) a. 75 m/s on a bearing of 295 to Cartesian form b. [3, 8] to direction/magnitude form 6. Express as a single vector: (4 marks) a. P3 + SR b. EF DF _._\\A_._\\_._\\ c. MPQR+NMRP 7. Demonstrate using diagrams; (4 marks) a. that vector addition is commutative ie. 6' + j = j + E' b. that vector addition is associative ie. E' + (? + f') = (3' + ?) + f' 8. Research an example of the use of vectors and explain how the mathematics is used, for example in engineering, computer animation, gaming, 3-D printing or GPS technology. (5 marks)