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. PS + SR b. EF DF c. MP - QR + NM - RP 7. Demonstrate using diagrams; (4 marks) a, that vector addition is commutative le. a + b - b + a b. that vector addition is associative ie. a + ( b + c ) - (a + 62. In the diagram, ACE is an equilateral triangle. Vertices B, D, and F are the midpoints of AC CE, and EA and AB = u and AF = U. (6 marks) Write the following in terms of u and U . D a. AC b. AD c. CE d. EB A B Give an example of a vector that is equal to: e. 2VGive an example of a vector that is equal to: e. 2v f. u - V 3. Draw diagrams to show two vectors a and b and the vectors a + b and a - b. (6 marks) a. When is the magnitude of a + b more than that of a - b ? b. When is the magnitude of a + b less than that of a - b? c. When is the magnitude of a + b equal to that of a - b ? When is a + b - a | + 6 ? e. When is the minimum value of | a + b ? 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)